2015 AP Biology free response 2 c d

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Part c.

00:00:01.734 --> 00:00:04.985
A researcher estimates
that in a certain organism,

00:00:04.985 --> 00:00:09.243
the complete metabolism or
glucose produces 30 molecules

00:00:09.243 --> 00:00:12.592
of ATP for each molecule of glucose.

00:00:12.592 --> 00:00:16.005
The energy released from the
total oxidation of glucose

00:00:16.005 --> 00:00:20.996
under standard condition is
686 kilocalories per mole.

00:00:20.996 --> 00:00:24.717
The energy released from
the hydrolysis of ATP to ADP

00:00:24.717 --> 00:00:27.090
and inorganic phosphate
under standard conditions

00:00:27.090 --> 00:00:29.723
is 7.3 kilocalories per mole.

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Calculate the amount of energy available

00:00:31.706 --> 00:00:34.956
from the hydrolysis of 30 moles of ATP.

00:00:35.999 --> 00:00:39.347
Calculate the efficiency
of total ATP production

00:00:39.347 --> 00:00:42.596
from one mole of glucose in the organism.

00:00:42.596 --> 00:00:45.067
Describe what happens to the excess energy

00:00:45.067 --> 00:00:47.993
that is released from the
metabolism of glucose.

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All right, I'm tired of squeezing things

00:00:49.423 --> 00:00:51.212
in between the questions,
so let me go down here

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to get some real estate.

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So let's do the first part.

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Let's calculate the
amount of energy available

00:00:56.867 --> 00:01:00.117
from the hydrolysis of 30 moles of ATP.

00:01:01.614 --> 00:01:02.783
So let me write this.

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Hydrolysis.

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Hydrolysis of

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30 moles

00:01:11.754 --> 00:01:12.587
of ATP.

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So I'll draw this, and we've
got the title right over there.

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So let's just take 30 moles,

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30, 30 moles

00:01:22.723 --> 00:01:23.807
of ATP times,

00:01:25.374 --> 00:01:28.120
they tell us how much energy is released

00:01:28.120 --> 00:01:31.338
when you hydrolyze that ATP per mole.

00:01:31.338 --> 00:01:34.685
They say, the energy released
from the hydrolysis of ATP,

00:01:34.685 --> 00:01:35.953
let me underline that.

00:01:35.953 --> 00:01:39.399
The energy released from
the hydrolysis of ATP to ADP

00:01:39.399 --> 00:01:41.902
and inorganic phosphate
under standard conditions

00:01:41.902 --> 00:01:44.405
is 7.3 kilocalories per mole.

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We have 30 moles,

00:01:46.451 --> 00:01:50.449
it's getting hyd, that
is undergoing hydrolysis,

00:01:50.449 --> 00:01:53.699
and so 30 moles times 7.3 kilocalories,

00:01:56.335 --> 00:01:58.168
kilocalories per mole.

00:01:59.324 --> 00:02:01.242
And what is that going to be equal to?

00:02:01.242 --> 00:02:02.997
Well the moles cancel with the moles.

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The units are going to be kilocalories,

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which makes sense, because
I want units of energy.

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And what is 30 times 7.3?

00:02:08.914 --> 00:02:11.580
See, three times 7.3 would be 21.9,

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so this is going to be 219,

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since this is 30 times 7.3.

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219 kilocalories.

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All right.

00:02:20.260 --> 00:02:21.592
Now let's do the second part.

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I'll do this in a different color.

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If you're actually taking the test,

00:02:23.856 --> 00:02:26.470
you know I might get the
benefit of multiple colors,

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but this is for you, to help me help you

00:02:29.375 --> 00:02:30.500
understand what's going on.

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Calculate the efficiency
of total ATP production

00:02:33.101 --> 00:02:36.518
from one mole of glucose in the organism.

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So I'll do that over here.

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Efficiency.

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Efficiency is,

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actually let me do it,

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well, efficiency is equal to

00:02:48.801 --> 00:02:51.801
energy is going to be energy in ATP,

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energy stored

00:02:58.130 --> 00:02:58.963
in ATP,

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over total energy,

00:03:03.921 --> 00:03:06.255
total energy from oxidation,

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energy from oxidation

00:03:13.797 --> 00:03:14.713
of glucose.

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So they say calculate the efficiency

00:03:19.292 --> 00:03:21.761
of total AT production, ATP production,

00:03:21.761 --> 00:03:23.354
from one mole of glucose in the organism.

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So this is going to be equal to.

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So they tell us what the energy production

00:03:27.787 --> 00:03:31.479
when you oxidize one mole of glucose.

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They say it is 686 kilocalories per mole.

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So the denominator here
is 686 kilocalories

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and the numerator, the
energy stored in ATP,

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well, for this particular organism,

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it is able to produce 30 ATPs.

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The complete metabolism of glucose

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produces 30 molecules of ATP.

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So for every mole of glucose,

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it's producing 30 moles of ATP.

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And so we already figured

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that's going to be 219 kilocalories.

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219 kilocalories.

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So now we just have to do
a little bit of math here,

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figure out what 219 divided
by 686 is going to be.

00:04:08.733 --> 00:04:10.357
Let me do it over here.

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686 divided by 200, oh, sorry,

00:04:15.007 --> 00:04:16.590
219 divided by 686.

00:04:18.095 --> 00:04:20.629
This is going to be less than zero.

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So let me go straight to, how many times

00:04:22.450 --> 00:04:24.450
would 686 go into 2,190?

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Well, this is a little bit less than 700

00:04:31.098 --> 00:04:32.592
and seven times three is 21,

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so this looks, it's about three times.

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Three times six is 18.

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Three times eight is 24 plus one is 25.

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Three times six is 18 plus two is 20.

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Let me subtract it.

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Let's see.

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90 minus 58 is 32.

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So I have 132

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Then I can bring down another zero.

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686, well, let's see.

00:04:59.378 --> 00:05:01.494
It looks like this might
be one or two times.

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Let's see, two times 686 would be 1,200,

00:05:04.933 --> 00:05:06.721
this is actually going to be one time,

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by feeling, or maybe we'll
round up, it sounds like

00:05:10.135 --> 00:05:12.135
So one times 686 is 686.

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You subtract.

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All right, I will do some regrouping here.

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So I can make this a 10,

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this a one.

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So 10 minus six is four.

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Now I can make this a two and this an 11.

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11 minus eight is three.

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And then 12 minus six is six.

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So, 686 goes into 6,340,

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this is definitely going
to be more than 5 times.

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So if we want to approximate,
we would round up.

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This is going to be approximate,

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so this going to be something else

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that is greater than five,

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so it's going to be approximately 32%.

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So I could write it, let me write it here.

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So this is approximately 32% efficiency.

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So roughly 32% of the potential energy,

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or of all the energy that can be produced

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from the oxidation of glucose

00:06:04.718 --> 00:06:07.449
actually ends up getting stored in ATP.

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Now, they say describe what happens,

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I want this in another color for fun.

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Describe what happens to the excess energy

00:06:13.950 --> 00:06:16.551
that is released from the
metabolism of glucose.

00:06:16.551 --> 00:06:17.851
Yeah, what happens to,

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what happens to the
other 68% of the energy?

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So, I'll do it over here.

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The rest of the energy
is released as heat.

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The rest of energy

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gets converted, or goes,

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is released,

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released as heat.

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And you could say it's
also released as entropy,

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increasing the number of
possible states of the cells,

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more things are bouncing
around in different ways.

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But this is the easiest
way to think about it,

00:06:52.277 --> 00:06:53.122
it is released as heat.

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In general, when you think
about any thermodynamic process,

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if you think about the efficiency,

00:06:56.373 --> 00:06:57.617
and you think about,
well, where is all of that

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lost energy that wasn't captured,

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it's usually going to be,

00:07:01.421 --> 00:07:04.509
it's usually going to be heat.

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All right, now let's do part d.

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Part d.

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The enzymes of the Krebs cycle function

00:07:10.393 --> 00:07:13.973
in the cytosol of bacteria,
but among eukaryotes,

00:07:13.973 --> 00:07:18.655
the enzymes function
mostly in the mitochondria.

00:07:18.655 --> 00:07:21.650
All right, mostly in the
mitochondria, an organelle.

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Pose a scientific question that connects

00:07:23.861 --> 00:07:27.664
the subcellular location of
the enzymes in the Krebs cycle

00:07:27.664 --> 00:07:31.012
to the evolution of eukaryotes.

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All right, well, we've talked about it,

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when we first talk about
mitochondria on Khan Academy,

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but there actually is a
theory that mitochondria,

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or the ancestors of mitochondria,

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might have been independent,
prokaryotic organisms.

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So we could say, the scientific question,

00:07:50.303 --> 00:07:52.220
we could say, were the

00:07:54.116 --> 00:07:54.949
ancestors

00:07:57.237 --> 00:07:58.570
of mitochondria,

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mitochondria

00:08:03.998 --> 00:08:05.498
once independent,

00:08:09.200 --> 00:08:10.866
in-de, independent,

00:08:14.178 --> 00:08:15.178
independent,

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we could even say, well, prokaryotic,

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prokaryotic, kary-otic

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organisms

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whose descendants lived, learned,

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whose descendants became incorporated

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in euakaryotic organisms?

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Whose descendants,

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descendants, de,

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descend, descendants,

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whose descendants

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became, became incorporated,

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became incorporated, corp-or-ated

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inside eukaryotes,

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eukaryotes.

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So that's a scientific question,

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and a really interesting one,

00:09:09.498 --> 00:09:11.221
that, you know, if you look at any cell

00:09:11.221 --> 00:09:13.887
in the human body,
you're actually going to,

00:09:13.887 --> 00:09:15.870
you're going to see these mitochondria,

00:09:15.870 --> 00:09:17.658
or actually in the
great majority of cells,

00:09:17.658 --> 00:09:21.201
and were their ancestors
once independent organisms

00:09:21.201 --> 00:09:23.839
that now have, whose
descendants now live in

00:09:23.839 --> 00:09:25.529
symbiosis with our cells

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because they're so good
at the Krebs cycle?


2015 AP Biology free response 1 a c

WEBVTT
Kind: captions
Language: en

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- [Voiceover] "Many species
have circadian rhythms

00:00:02.340 --> 00:00:05.390
"that exhibit an
approximately 24-hour cycle.

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"Circadian rhythms are
controlled by both genetics

00:00:08.460 --> 00:00:11.175
"and environmental
conditions, including light.

00:00:11.175 --> 00:00:13.610
"Researchers investigated
the effect of light

00:00:13.610 --> 00:00:16.520
"on mouse behavior by
using a running wheel

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"with a motion sensor to record activity

00:00:19.080 --> 00:00:22.070
"on actograms, as shown in figure one."

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All right, so let's think
about what figure one

00:00:23.850 --> 00:00:25.300
is showing us.

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We have a picture of a mouse here

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that seems to be inactive,

00:00:28.530 --> 00:00:29.900
definitely not on the running wheel,

00:00:29.900 --> 00:00:32.000
even eyes closed, maybe it's sleeping.

00:00:32.000 --> 00:00:33.680
And then here, a picture of a mouse

00:00:33.680 --> 00:00:35.600
that is on the running
wheel, maybe running,

00:00:35.600 --> 00:00:37.186
with its eyes open.

00:00:37.186 --> 00:00:40.280
And then we see our actogram
here and it describes,

00:00:40.280 --> 00:00:42.760
"Strategy for recording
mouse activity data.

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"When a mouse is active
on the running wheel,

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"the activity is recorded
as a dark horizontal line

00:00:49.340 --> 00:00:50.460
"on an actogram.

00:00:50.460 --> 00:00:52.080
"When the mouse is inactive,

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"no dark line is recorded."

00:00:53.680 --> 00:00:57.440
So we can see here, it gives
us the activity for each day.

00:00:57.440 --> 00:01:01.133
So for day one, day
one is right over here.

00:01:01.133 --> 00:01:02.480
Let me do that in a lighter color

00:01:02.480 --> 00:01:05.730
so that I don't overwrite
what you need to see.

00:01:05.730 --> 00:01:07.590
So day one is right over there,

00:01:07.590 --> 00:01:10.820
and you can see from hour zero to hour 12,

00:01:10.820 --> 00:01:14.920
since we have no black
line, the mouse is inactive.

00:01:14.920 --> 00:01:17.440
We're not detecting activity
on the running wheel.

00:01:17.440 --> 00:01:19.940
And then when we have the
black line from hour 12

00:01:19.940 --> 00:01:23.200
to hour 24, that means
we are detecting activity

00:01:23.200 --> 00:01:25.040
on the running wheel and so we can assume

00:01:25.040 --> 00:01:27.240
that the mouse is active.

00:01:27.240 --> 00:01:28.760
And then we have it again for day two,

00:01:28.760 --> 00:01:30.120
and the way this is set up, it looks like

00:01:30.120 --> 00:01:32.920
that pattern holds for every day.

00:01:32.920 --> 00:01:34.340
Let's keep going.

00:01:34.340 --> 00:01:36.870
"For the investigation,

00:01:38.340 --> 00:01:42.020
"adult male mice were
individually housed in cages

00:01:42.020 --> 00:01:45.640
"in a soundproof room
at 25 degrees Celsius."

00:01:45.640 --> 00:01:47.640
So they wanted to make
sure that these mice

00:01:47.640 --> 00:01:48.880
didn't bother each other,

00:01:48.880 --> 00:01:51.050
that this was definitely
controlled conditions.

00:01:51.050 --> 00:01:54.340
Soundproof, that they're not
impacted by outside noises,

00:01:54.340 --> 00:01:56.860
other mice, a variation in temperature,

00:01:56.860 --> 00:01:59.146
so they tried to for all of these things.

00:01:59.146 --> 00:02:01.520
"Each mouse was provided
with adequate food,

00:02:01.520 --> 00:02:04.740
"water, bedding material,
and a running wheel.

00:02:04.740 --> 00:02:07.040
"The mice were exposed to daily periods

00:02:07.040 --> 00:02:08.580
"of 12 hours of light,"

00:02:08.580 --> 00:02:09.530
with the capital L,

00:02:09.530 --> 00:02:10.720
"and 12 hours of dark,"

00:02:10.720 --> 00:02:11.450
capital D.

00:02:11.450 --> 00:02:12.540
L12, D12.

00:02:12.540 --> 00:02:15.340
So that's 12 hours of
light, 12 hours of darkness,

00:02:15.340 --> 00:02:17.490
"for 14 days, and their activity

00:02:17.490 --> 00:02:19.366
"was continuously monitored.

00:02:19.366 --> 00:02:22.660
"The activity data are
shown in figure two."

00:02:22.660 --> 00:02:25.120
All right, so this is an
actogram of mouse activity

00:02:25.120 --> 00:02:27.070
under L12, D12 conditions.

00:02:27.070 --> 00:02:29.290
Each row represents a 24-hour period

00:02:29.290 --> 00:02:31.500
and the dark horizontal
lines represent activity

00:02:31.500 --> 00:02:33.431
on the running wheel,
just like we saw before.

00:02:33.431 --> 00:02:36.240
But this is actual data
that we are recording.

00:02:36.240 --> 00:02:40.040
So in the first 12 hours,
the mouse are in conditions

00:02:40.040 --> 00:02:42.530
where there's light, and you
can see for the most part,

00:02:42.530 --> 00:02:45.420
on day one, we detect no activity.

00:02:45.420 --> 00:02:47.640
On day two, we also detective no activity.

00:02:47.640 --> 00:02:49.820
On day three, we detect
a little bit of activity,

00:02:49.820 --> 00:02:52.070
but for the most part, when it's light,

00:02:52.070 --> 00:02:54.900
we detect very little to no activity.

00:02:54.900 --> 00:02:56.810
And when it's dark, it's the opposite.

00:02:56.810 --> 00:02:59.770
We detect a lot of activity
on that running wheel.

00:02:59.770 --> 00:03:02.620
There's a few gaps right over here,

00:03:02.620 --> 00:03:06.914
but for the most part, the
mouse is active when it's dark.

00:03:06.914 --> 00:03:11.390
So the mouse is active when it's dark

00:03:11.390 --> 00:03:14.912
and inactive

00:03:14.912 --> 00:03:17.020
when it is light, which is the opposite

00:03:17.020 --> 00:03:19.760
of most human beings, or frankly,

00:03:19.760 --> 00:03:22.120
well, definitely human beings,
where we tend to be active

00:03:22.120 --> 00:03:24.240
in the light and inactive in the dark.

00:03:24.240 --> 00:03:25.787
Interesting.

00:03:25.787 --> 00:03:29.690
After 14 days, so that was
just with 12 hours of light,

00:03:29.690 --> 00:03:31.106
12 hours of darkness.

00:03:31.106 --> 00:03:33.320
"After 14 days of L12, D12,"

00:03:33.320 --> 00:03:35.400
so it's 12 hours of
light, 12 hours darkness,

00:03:35.400 --> 00:03:38.400
"the mice were placed
in continuous darkness."

00:03:38.400 --> 00:03:39.660
Capital D, capital D.

00:03:39.660 --> 00:03:41.140
DD, that sounds unpleasant.

00:03:41.140 --> 00:03:42.720
Continuous darkness.

00:03:42.720 --> 00:03:44.480
And their activity on the running wheel

00:03:44.480 --> 00:03:46.215
was reported as before.

00:03:46.215 --> 00:03:50.220
"The activity data under
DD," continuous darkness,

00:03:50.220 --> 00:03:52.503
"conditions are shown in figure three."

00:03:52.503 --> 00:03:55.230
All right, so this is interesting here.

00:03:55.230 --> 00:03:57.140
So it looks like on day one,

00:03:57.140 --> 00:03:59.970
the mice were inactive, not 12 hours,

00:03:59.970 --> 00:04:01.800
like we saw when we had 12 hours of light,

00:04:01.800 --> 00:04:04.270
but it looks like about 10 hours.

00:04:04.270 --> 00:04:07.660
And then from hour, I don't
know, this is maybe hour nine

00:04:07.660 --> 00:04:09.870
or 10, to about hour,

00:04:09.870 --> 00:04:11.990
it looks like maybe hour 21,

00:04:11.990 --> 00:04:13.940
they were active.

00:04:14.840 --> 00:04:17.560
Maybe 12 hours, maybe a
little less than 12 hours.

00:04:17.560 --> 00:04:21.040
And then inactive,
active, inactive, active,

00:04:21.040 --> 00:04:24.990
but it seems to be less than for 12 hours.

00:04:24.990 --> 00:04:27.280
And then they're active
for less than 12 hours.

00:04:27.280 --> 00:04:30.080
So you see everything shifting
up every 24-hour period

00:04:30.080 --> 00:04:32.440
because they tend to be
inactive for less than 12 hours.

00:04:32.440 --> 00:04:34.680
It looks like it's 10
or 11 hours each day.

00:04:34.680 --> 00:04:38.140
And then active for a little
bit less than 12 hours.

00:04:38.140 --> 00:04:40.390
So that's why you see
this shifting pattern

00:04:40.390 --> 00:04:43.442
where every day the activity starts

00:04:43.442 --> 00:04:45.340
at roughly an earlier period.

00:04:45.340 --> 00:04:46.940
It's not a perfect trend,

00:04:46.940 --> 00:04:49.450
but you see the trend over multiple days.

00:04:49.450 --> 00:04:52.090
I can draw, I can show a line

00:04:52.090 --> 00:04:53.340
that goes something like this.

00:04:53.340 --> 00:04:56.150
You can see every day
we are starting activity

00:04:56.150 --> 00:04:58.046
at an earlier hour.

00:04:58.046 --> 00:05:00.780
And every day we're
also ending our activity

00:05:00.780 --> 00:05:02.400
at an earlier hour.

00:05:02.400 --> 00:05:04.410
And there's a lot more,
I guess you could say,

00:05:04.410 --> 00:05:06.360
sporadic activity going on.

00:05:06.360 --> 00:05:10.120
And remember, this under
continuous darkness.

00:05:10.120 --> 00:05:12.260
All right, let's see if we
can answer the questions.

00:05:13.380 --> 00:05:15.800
"The nervous system plays
a role in coordinating

00:05:15.800 --> 00:05:17.900
"the observed activity pattern of mice

00:05:17.900 --> 00:05:20.320
"in response to light-dark stimuli."

00:05:20.320 --> 00:05:22.140
Yes, that makes sense, of course.

00:05:22.140 --> 00:05:23.740
"Describe one role of each

00:05:23.740 --> 00:05:25.560
"of the following anatomical structures

00:05:25.560 --> 00:05:29.210
"in responding to light-dark stimuli."

00:05:29.210 --> 00:05:32.144
A photoreceptor in the retina of an eye.

00:05:32.144 --> 00:05:34.000
Well, this detects light.

00:05:36.510 --> 00:05:38.200
Detects light

00:05:39.190 --> 00:05:40.830
and sends signal.

00:05:42.190 --> 00:05:44.240
Or maybe I'll say transmit signal.

00:05:48.640 --> 00:05:50.715
Transmits signal

00:05:50.715 --> 00:05:52.704
that eventually gets to brain.

00:05:52.704 --> 00:05:55.580
That eventually

00:05:57.390 --> 00:05:59.470
gets to brain.

00:05:59.470 --> 00:06:02.766
Gets to the brain.

00:06:02.766 --> 00:06:03.660
All right?

00:06:03.660 --> 00:06:04.720
The brain.

00:06:04.720 --> 00:06:06.860
Well, it receives signals.

00:06:06.860 --> 00:06:08.510
It receives.

00:06:10.060 --> 00:06:12.700
I before E, except after C.

00:06:12.700 --> 00:06:15.682
It re-see (laughs), it receives,

00:06:15.682 --> 00:06:18.120
it receives signals.

00:06:19.280 --> 00:06:23.580
It receives signals and
then coordinates activity

00:06:23.580 --> 00:06:24.680
based on that.

00:06:28.220 --> 00:06:31.060
Coordinates activity

00:06:32.700 --> 00:06:35.340
response based on that.

00:06:36.540 --> 00:06:39.030
Based on signals.

00:06:39.030 --> 00:06:42.520
Based on the signals.

00:06:42.520 --> 00:06:44.140
So this is really just, you know,

00:06:44.140 --> 00:06:45.760
do we know what a photoreceptor,

00:06:45.760 --> 00:06:47.100
a brain, and a motor neuron,

00:06:47.100 --> 00:06:49.954
I guess as related to this test.

00:06:49.954 --> 00:06:51.460
And then a motor neuron,

00:06:51.460 --> 00:06:53.860
well, these are neurons
that would stimulate.

00:06:53.860 --> 00:06:56.634
You tend to think of things
that would be, you know,

00:06:56.634 --> 00:06:59.120
like motor movement, like muscles,

00:06:59.120 --> 00:07:01.060
but they also control things like glands.

00:07:01.060 --> 00:07:02.620
So they stimulate

00:07:06.220 --> 00:07:10.588
muscles, glands.

00:07:10.588 --> 00:07:12.930
And glands could be
especially relevant here

00:07:12.930 --> 00:07:14.440
because glands might be the things

00:07:14.440 --> 00:07:17.140
that release or don't release hormones

00:07:17.140 --> 00:07:19.999
that might put the mice
to sleep or wake them up.

00:07:19.999 --> 00:07:21.440
Glands

00:07:23.200 --> 00:07:27.270
that might release
hormones related to sleep.

00:07:27.270 --> 00:07:31.860
Might release hormones

00:07:33.510 --> 00:07:35.670
related to sleep, wake.

00:07:35.670 --> 00:07:37.030
Related

00:07:37.950 --> 00:07:40.366
to sleep

00:07:40.366 --> 00:07:42.400
and activity.

00:07:43.430 --> 00:07:45.280
All right, so I think that's,

00:07:45.280 --> 00:07:48.140
we've taken a decent job
of describing the role

00:07:48.140 --> 00:07:50.170
of each of those.

00:07:50.170 --> 00:07:52.830
All right, let's go to part B now.

00:07:52.830 --> 00:07:55.910
"Based on an analysis of
the data in figure two,

00:07:55.910 --> 00:07:58.670
"describe the activity pattern of mice

00:07:58.670 --> 00:08:01.860
"during the light and dark periods

00:08:01.860 --> 00:08:04.974
"of the L12, D12 cycle."

00:08:04.974 --> 00:08:06.760
Well, this was pretty straightforward.

00:08:06.760 --> 00:08:08.604
When there was light,

00:08:08.604 --> 00:08:11.542
so they were inactive during light.

00:08:11.542 --> 00:08:13.000
Inactive

00:08:14.000 --> 00:08:17.460
during light.

00:08:19.240 --> 00:08:21.540
Active during dark.

00:08:22.580 --> 00:08:23.680
Active

00:08:26.320 --> 00:08:28.260
during dark.

00:08:28.260 --> 00:08:30.090
I could've written the answer down below,

00:08:30.090 --> 00:08:31.580
but I think I could've
squeezed this one in.

00:08:31.580 --> 00:08:32.960
That's the basic idea.

00:08:32.960 --> 00:08:36.760
L12, D12 cycle, we saw right over here.

00:08:36.760 --> 00:08:38.750
Inactive during light,

00:08:38.750 --> 00:08:41.838
and then active during the dark.

00:08:41.838 --> 00:08:43.526
All right.

00:08:43.526 --> 00:08:45.915
Active during the dark.

00:08:45.915 --> 00:08:47.390
Okay.

00:08:48.620 --> 00:08:51.610
"The researchers claim that
the genetically controlled

00:08:51.610 --> 00:08:54.260
"circadian rhythm in
the mice does not follow

00:08:54.260 --> 00:08:56.774
"a 24-hour cycle.

00:08:56.774 --> 00:08:59.700
"Describe one difference
between the daily pattern

00:08:59.700 --> 00:09:02.488
"of activity under L12, D12 conditions,

00:09:02.488 --> 00:09:03.940
"figure two, and under,"

00:09:03.940 --> 00:09:06.800
continuous darkness, the DD
conditions in figure three.

00:09:06.800 --> 00:09:09.730
And "use data to support
the researchers' claim."

00:09:09.730 --> 00:09:11.940
All right, well, we
talked about this already.

00:09:16.080 --> 00:09:19.580
So under DD,

00:09:20.680 --> 00:09:23.510
mice active

00:09:27.040 --> 00:09:28.870
and inactive

00:09:31.110 --> 00:09:33.686
for less

00:09:33.686 --> 00:09:36.700
than 24,

00:09:36.700 --> 00:09:38.815
or less than 12 hours each.

00:09:38.815 --> 00:09:42.900
12 hours each.

00:09:42.900 --> 00:09:47.720
And then we could say versus 12 hours

00:09:49.040 --> 00:09:50.560
inactivity

00:09:53.270 --> 00:09:55.255
under light,

00:09:55.255 --> 00:09:57.762
under, I could say, L12.

00:09:57.762 --> 00:10:02.480
And 12 hours activity

00:10:04.820 --> 00:10:07.662
under D,

00:10:07.662 --> 00:10:09.320
under D12.

00:10:09.320 --> 00:10:10.850
So under continuous darkness,

00:10:10.850 --> 00:10:13.590
mice active and inactive
for less than 12 hours each

00:10:13.590 --> 00:10:16.400
versus 12 hours inactivity under L12

00:10:16.400 --> 00:10:18.700
and to 12 hours activity under D12

00:10:18.700 --> 00:10:20.590
when it was dark for 12 hours.

00:10:22.180 --> 00:10:24.416
So less than

00:10:24.416 --> 00:10:25.750
24-hour cycle.

00:10:25.750 --> 00:10:27.350
So less than

00:10:29.420 --> 00:10:31.660
24-hour cycle.

00:10:32.670 --> 00:10:36.240
Activity also more sporadic.

00:10:36.240 --> 00:10:37.500
Activity

00:10:39.400 --> 00:10:42.183
also more

00:10:42.183 --> 00:10:43.600
sporadic.

00:10:44.960 --> 00:10:48.627
Sporadic, or we could say less continuous.

00:10:48.627 --> 00:10:51.280
Less continuous, there's
definitely more times

00:10:51.280 --> 00:10:54.200
where the activity periods is broken up

00:10:54.200 --> 00:10:55.640
by inactivity or the inactive periods

00:10:55.640 --> 00:10:56.810
is broken up by activity.

00:10:56.810 --> 00:10:58.310
Less continuous.

00:10:59.720 --> 00:11:01.900
All right, I feel pretty good about that.

00:11:01.900 --> 00:11:02.870
Now, let's see.

00:11:02.870 --> 00:11:05.720
Actually, since I'm already
at 11 minutes in this video,

00:11:05.720 --> 00:11:10.100
I'll continue the next two
parts in the next video.


2015 AP Biology free response 1 d e

WEBVTT
Kind: captions
Language: en

00:00:00.197 --> 00:00:02.177
- [Voiceover] All right, Part D.

00:00:02.177 --> 00:00:04.837
To investigate the claim
that exposure to light

00:00:04.837 --> 00:00:08.581
overrides the genetically-controlled
circadian rhythm,

00:00:08.581 --> 00:00:10.873
the researchers plan to
repeat the experiment

00:00:10.873 --> 00:00:12.972
with mutant mice lacking a gene

00:00:12.972 --> 00:00:15.525
that controls the circadian rhythm.

00:00:15.525 --> 00:00:17.903
Predict the observed activity pattern

00:00:17.903 --> 00:00:21.374
of the mutant mice
under L12:D12 conditions

00:00:21.374 --> 00:00:24.607
and under DD, continuous
darkness conditions,

00:00:24.607 --> 00:00:27.494
that would support the
claim that light overrides

00:00:27.494 --> 00:00:30.596
the genetically-controlled
circadian rhythm.

00:00:30.596 --> 00:00:34.134
All right, so let me write
this down. So, Part D.

00:00:34.134 --> 00:00:37.222
So under some mutant mice,

00:00:37.222 --> 00:00:41.152
mutant mice,

00:00:41.152 --> 00:00:43.587
under, so let me make two columns,

00:00:43.587 --> 00:00:46.872
mutant mice under L12,

00:00:46.872 --> 00:00:50.152
L12:D12, and then

00:00:50.152 --> 00:00:55.054
under continuous, continuous
darkness, what would I expect?

00:00:55.054 --> 00:00:56.870
What would I expect?

00:00:56.870 --> 00:00:59.155
So they predict the
observed activity pattern.

00:00:59.155 --> 00:01:01.183
So the mutant mice, they don't have,

00:01:01.183 --> 00:01:04.087
they have some, they're lacking genes

00:01:04.087 --> 00:01:07.286
that control circadian
rhythm, but under L12:D12,

00:01:07.286 --> 00:01:10.496
they don't need the
genetic circadian patterns,

00:01:10.496 --> 00:01:13.119
the genetically-influenced
ones, because they get the ones

00:01:13.119 --> 00:01:15.663
from their environment,
the light and the darkness.

00:01:15.663 --> 00:01:17.518
They didn't get, this isn't a gene

00:01:17.518 --> 00:01:20.157
that somehow makes them
not sensitive to light.

00:01:20.157 --> 00:01:23.510
So I would assume under the L12:D12,

00:01:23.510 --> 00:01:26.364
they would behave, they
would have activity pattern

00:01:26.364 --> 00:01:30.982
similar to non-mutant mice, activity

00:01:32.082 --> 00:01:36.100
same as non-mutant,

00:01:36.100 --> 00:01:41.020
as non-mutant,

00:01:41.020 --> 00:01:44.927
mutant mice,

00:01:44.927 --> 00:01:49.890
non, or inactivity, inactivity

00:01:49.890 --> 00:01:54.468
during L12,

00:01:54.468 --> 00:01:59.442
activity, activity

00:02:00.612 --> 00:02:04.591
during D12.

00:02:04.591 --> 00:02:05.707
That's what I would expect.

00:02:05.707 --> 00:02:07.356
They still could react to the light

00:02:07.356 --> 00:02:08.394
and the darkness the same way

00:02:08.394 --> 00:02:10.119
that a non-mutant mice would.

00:02:10.119 --> 00:02:12.084
Now, what about continuous darkness?

00:02:12.084 --> 00:02:14.215
The non-mutant mice, we said that they,

00:02:14.215 --> 00:02:16.533
they went off of a 24-hour cycle,

00:02:16.533 --> 00:02:18.994
but they still had a cycle
where they were inactive,

00:02:18.994 --> 00:02:23.350
active, inactive, active,
and it was less than 12 hours

00:02:23.350 --> 00:02:25.367
for each cycle, but it was close to it.

00:02:25.367 --> 00:02:28.149
It was maybe 9, 10, or
11 hours of activity,

00:02:28.149 --> 00:02:31.354
followed by 9, 10, or
11 hours of inactivity.

00:02:31.354 --> 00:02:33.135
I would guess that a mutant mouse

00:02:33.135 --> 00:02:35.466
that has no, that doesn't have some

00:02:35.466 --> 00:02:37.841
of these genes for circadian rhythm,

00:02:37.841 --> 00:02:39.409
well, for them, it's just gonna be,

00:02:39.409 --> 00:02:40.486
it's just gonna be random,

00:02:40.486 --> 00:02:43.090
it's just gonna be much more sporadic.

00:02:43.090 --> 00:02:47.353
So, much, much

00:02:47.353 --> 00:02:51.491
more sporadic,

00:02:51.491 --> 00:02:54.779
sporadic activity,

00:02:54.779 --> 00:02:59.779
activity, fewer,

00:02:59.836 --> 00:03:03.370
fewer continuous,

00:03:03.370 --> 00:03:05.610
continuous,

00:03:05.610 --> 00:03:08.925
or I would say, maybe,
less continuous periods,

00:03:08.925 --> 00:03:12.036
or shorter continuous periods,

00:03:12.036 --> 00:03:16.289
shorter continuous

00:03:16.289 --> 00:03:20.912
periods of activity

00:03:20.912 --> 00:03:22.896
and inactivity,

00:03:22.896 --> 00:03:25.165
activity slash

00:03:25.165 --> 00:03:29.016
inactivity.

00:03:29.016 --> 00:03:32.798
All right, now let's look at Part E now.

00:03:32.798 --> 00:03:35.652
So that was my predictions
that I would see

00:03:35.652 --> 00:03:37.316
for mutant mice in either of these.

00:03:37.316 --> 00:03:39.664
So now let's go to Part E.

00:03:39.664 --> 00:03:42.172
In nature, mice are potential prey

00:03:42.172 --> 00:03:46.109
for some predatory birds
that hunt during the day.

00:03:46.109 --> 00:03:49.667
Describe two features of
a model that represents

00:03:49.667 --> 00:03:51.748
how the predator-prey relationship

00:03:51.748 --> 00:03:55.202
between the birds and the
mice may have resulted

00:03:55.202 --> 00:03:56.705
in the evolution

00:03:56.705 --> 00:04:01.304
of the observed activity pattern of mice.

00:04:01.304 --> 00:04:06.304
Well, if the birds hunt during the day,

00:04:06.433 --> 00:04:11.174
if birds hunt

00:04:11.174 --> 00:04:15.617
during day

00:04:15.617 --> 00:04:16.697
a mouse is more likely

00:04:16.697 --> 00:04:21.275
to be eaten by a bird if
it's active during the day.

00:04:21.275 --> 00:04:25.052
Mouse, then,

00:04:25.052 --> 00:04:29.337
then the mouse

00:04:29.337 --> 00:04:34.277
is more likely

00:04:34.277 --> 00:04:38.536
to be eaten,

00:04:38.536 --> 00:04:42.510
eaten if it is

00:04:42.510 --> 00:04:44.398
active during the day,

00:04:44.398 --> 00:04:47.036
if it is active

00:04:47.036 --> 00:04:51.987
during the day.

00:04:53.548 --> 00:04:54.721
And if it is, I guess you could say

00:04:54.721 --> 00:04:57.440
that's one, that's one
feature of our model,

00:04:57.440 --> 00:04:59.761
that you're just more likely to be eaten

00:04:59.761 --> 00:05:02.009
if you're active when
the birds are hunting.

00:05:02.009 --> 00:05:03.969
And then the second one
is, if you're more likely

00:05:03.969 --> 00:05:08.268
to be eaten, then you're
less likely to reproduce.

00:05:08.268 --> 00:05:11.350
If, actually that should be capital I,

00:05:11.350 --> 00:05:15.480
if, if the mouse

00:05:17.260 --> 00:05:22.172
is more likely

00:05:22.172 --> 00:05:25.422
to be eaten

00:05:25.422 --> 00:05:29.189
by being

00:05:29.189 --> 00:05:31.540
active

00:05:31.540 --> 00:05:35.755
during the day,

00:05:37.765 --> 00:05:40.727
then it is less likely to reproduce,

00:05:40.727 --> 00:05:44.628
then it is less

00:05:44.628 --> 00:05:46.728
likely

00:05:46.728 --> 00:05:49.393
to reproduce.

00:05:49.393 --> 00:05:53.091
And if I were, if I were
taking the AP test here,

00:05:53.091 --> 00:05:55.220
I would try to put as
much context as possible,

00:05:55.220 --> 00:05:56.435
because you're not exactly sure

00:05:56.435 --> 00:05:58.920
how they're, they're
going to mark this thing,

00:05:58.920 --> 00:06:01.544
to grade this thing, so
you could give more context

00:06:01.544 --> 00:06:04.646
that therefore, the mice

00:06:04.646 --> 00:06:06.852
that are active during,

00:06:06.852 --> 00:06:11.659
therefore, therefore,

00:06:11.659 --> 00:06:16.110
mice that are

00:06:16.110 --> 00:06:18.708
active

00:06:18.708 --> 00:06:21.348
during night,

00:06:21.348 --> 00:06:22.954
they have to be active sometime,

00:06:22.954 --> 00:06:27.075
active during night and inactive

00:06:28.185 --> 00:06:31.972
during day

00:06:31.972 --> 00:06:36.214
will be selected for, will

00:06:36.214 --> 00:06:40.520
be selected for,

00:06:41.370 --> 00:06:45.558
less likely to be eaten, less likely

00:06:45.558 --> 00:06:48.714
to be hunted,

00:06:48.714 --> 00:06:53.438
I guess you could say, and
more likely to reproduce,

00:06:53.438 --> 00:06:58.403
more likely to reproduce,

00:06:58.403 --> 00:07:02.535
reproduce, and we are done.


2015 AP Physics 1 free response 3d

WEBVTT
Kind: captions
Language: en

00:00:00.100 --> 00:00:01.264
- [Voiceover] All right, part d.

00:00:01.264 --> 00:00:02.651
Explain how any correct aspects

00:00:02.651 --> 00:00:05.066
of the student's reasoning
identified in part b

00:00:05.066 --> 00:00:09.362
are expressed by your mathematical
relationships in part c,

00:00:09.362 --> 00:00:11.823
and explain how your
relationship in part c correct,

00:00:11.823 --> 00:00:13.570
how your relationships in part c

00:00:13.570 --> 00:00:16.211
correct any incorrect aspects
of the student's reasoning

00:00:16.211 --> 00:00:17.425
identified in part b.

00:00:17.425 --> 00:00:18.308
It's a bit of a mouthful,

00:00:18.308 --> 00:00:19.107
but they're just saying,

00:00:19.107 --> 00:00:21.665
"Hey, kinda connect the
dots between part c"

00:00:21.665 --> 00:00:23.194
"and the two parts of part b."

00:00:23.194 --> 00:00:25.453
Refer to the relationships
you wrote in part c,

00:00:25.453 --> 00:00:26.753
not just the final answer you obtained

00:00:26.753 --> 00:00:29.394
by manipulating those relationships.

00:00:29.394 --> 00:00:30.735
And so we can,

00:00:30.735 --> 00:00:33.487
let me write it down here.

00:00:33.487 --> 00:00:34.578
So d.

00:00:34.578 --> 00:00:37.468
So part c

00:00:37.468 --> 00:00:40.997
shows us

00:00:40.997 --> 00:00:44.361
that doubling,

00:00:44.361 --> 00:00:47.801
doubling compression

00:00:49.031 --> 00:00:53.287
does result in more potential energy.

00:00:53.287 --> 00:00:57.987
Doubling compression does result

00:00:59.040 --> 00:01:03.498
in more,

00:01:03.498 --> 00:01:05.797
in more energy.

00:01:05.797 --> 00:01:08.258
And you could clarify that this is,

00:01:08.258 --> 00:01:11.207
this is potential,

00:01:11.207 --> 00:01:15.642
potential and kinetic

00:01:15.642 --> 00:01:17.476
at different points in time.

00:01:17.476 --> 00:01:19.636
And then we could even draw a line to it.

00:01:19.636 --> 00:01:21.424
So we see that,

00:01:21.424 --> 00:01:22.979
we see that right over here.

00:01:22.979 --> 00:01:25.563
That is, that is these,

00:01:25.563 --> 00:01:26.703
that line,

00:01:26.703 --> 00:01:29.179
and then that line right
over there shows that.

00:01:29.179 --> 00:01:32.299
So I could draw a bit of an arrow to it.

00:01:32.299 --> 00:01:35.757
They want us to reference
some of what we saw before.

00:01:35.757 --> 00:01:38.188
And just to make it clear,

00:01:38.188 --> 00:01:39.976
I can put in parentheses.

00:01:39.976 --> 00:01:44.053
I can show that U two
is equal to four U one,

00:01:44.053 --> 00:01:49.053
and that K two is equal to four,

00:01:49.102 --> 00:01:52.491
four K one.

00:01:52.491 --> 00:01:56.573
However, however,

00:01:58.158 --> 00:02:00.224
however,

00:02:00.224 --> 00:02:04.884
since the kinetic energy,

00:02:04.884 --> 00:02:09.320
since the kinetic

00:02:09.320 --> 00:02:12.402
energy

00:02:12.402 --> 00:02:17.332
is four times greater,

00:02:19.497 --> 00:02:24.000
and you have

00:02:26.300 --> 00:02:31.300
the same, same force of friction,

00:02:32.059 --> 00:02:36.447
force of friction,

00:02:36.447 --> 00:02:41.207
the distance is going to
be four times as long.

00:02:41.207 --> 00:02:44.151
The stopping distance,

00:02:45.480 --> 00:02:47.825
distance,

00:02:47.825 --> 00:02:50.472
is going to be four times as much.

00:02:50.472 --> 00:02:54.434
Is going to be

00:02:54.434 --> 00:02:58.979
four times as long.

00:03:00.123 --> 00:03:00.842
And even when we,

00:03:00.842 --> 00:03:02.282
so the correct parts.

00:03:02.282 --> 00:03:04.674
Part c shows us that
doubling the compression

00:03:04.674 --> 00:03:07.251
does result in more energy.

00:03:07.251 --> 00:03:11.068
And I could add and
more stopping distance.

00:03:11.068 --> 00:03:12.804
Let me do it there.

00:03:12.804 --> 00:03:17.753
And more stopping,

00:03:19.535 --> 00:03:23.289
stopping distance.

00:03:23.289 --> 00:03:24.179
Whoops.

00:03:24.179 --> 00:03:25.780
And more stopping distance.

00:03:25.780 --> 00:03:27.383
And the stopping distance,

00:03:27.383 --> 00:03:29.705
that arrow is easier to draw.

00:03:29.705 --> 00:03:32.491
And more stopping distance.

00:03:32.491 --> 00:03:36.276
However, since the kinetic
energy is four times greater,

00:03:36.276 --> 00:03:38.111
and you have the same force of friction,

00:03:38.111 --> 00:03:39.712
the stopping distance is going to be

00:03:39.712 --> 00:03:42.546
four times as long.

00:03:42.546 --> 00:03:45.050
And we saw that as well over there.

00:03:45.050 --> 00:03:45.893
So we're saying hey look,

00:03:45.893 --> 00:03:47.747
the student was right

00:03:47.747 --> 00:03:50.162
that more compression is more energy,

00:03:50.162 --> 00:03:51.346
more stopping distance.

00:03:51.346 --> 00:03:53.668
However, it's going to
be four times as long,

00:03:53.668 --> 00:03:55.270
the stopping distance,

00:03:55.270 --> 00:04:00.130
not two times

00:04:00.130 --> 00:04:02.081
as,

00:04:02.081 --> 00:04:03.798
not two times as far.

00:04:03.798 --> 00:04:05.690
And there you go.


2015 AP Physics 1 free response 3c

WEBVTT
Kind: captions
Language: en

00:00:00.193 --> 00:00:01.515
- [Voiceover] Alright,
now let's tackle part c.

00:00:01.515 --> 00:00:04.947
Use quantitative reasoning,
including equations as needed,

00:00:04.947 --> 00:00:06.571
to develop an expression

00:00:06.571 --> 00:00:08.882
for the new final position of the block.

00:00:08.882 --> 00:00:12.027
Express your answer in terms of D.

00:00:12.027 --> 00:00:15.546
Alright, I'm gonna set up a
little table here for part c.

00:00:15.546 --> 00:00:17.273
Oops, sorry about that.

00:00:17.273 --> 00:00:19.851
Sometimes my pen is not
functioning properly.

00:00:19.851 --> 00:00:22.187
Alright so part c.

00:00:22.187 --> 00:00:24.002
Let me set up two scenarios.

00:00:24.002 --> 00:00:27.318
So I have scenario one.

00:00:27.318 --> 00:00:32.318
Scenario one, where we
compress the spring,

00:00:32.822 --> 00:00:34.804
our delta x is equal to d,

00:00:34.804 --> 00:00:37.702
and then we have scenario two,

00:00:37.702 --> 00:00:42.702
scenario two, where we
compress the spring by

00:00:43.071 --> 00:00:45.737
twice as much, is equal to two d,

00:00:45.737 --> 00:00:48.089
and let me set up my table now,

00:00:48.089 --> 00:00:53.089
so, just like that and like this,

00:00:53.203 --> 00:00:54.772
and let's just think about a few things.

00:00:54.772 --> 00:00:56.821
So the first thing I wanna think about is

00:00:56.821 --> 00:01:01.821
the potential energy,
so the potential energy

00:01:02.022 --> 00:01:04.821
when the spring is compressed.

00:01:04.821 --> 00:01:09.821
So potential energy
when spring compressed.

00:01:15.302 --> 00:01:19.870
When, I'll just write
compressed, when compressed.

00:01:20.972 --> 00:01:24.555
Well in this scenario I'll
call it the potential energy

00:01:24.555 --> 00:01:28.230
for scenario one, it's
equal to one half times

00:01:28.230 --> 00:01:32.264
the spring constant, times how
much we compress it squared.

00:01:32.264 --> 00:01:34.163
Now what about scenario two?

00:01:34.163 --> 00:01:37.702
This potential energy
is going to be equal to

00:01:37.702 --> 00:01:41.246
one half times the spring
constant, times how much

00:01:41.246 --> 00:01:44.446
we compress it, it's now
twice as much, squared,

00:01:44.446 --> 00:01:47.758
well this is equal to one half
times the spring constant,

00:01:47.758 --> 00:01:51.703
times four d squared,

00:01:52.743 --> 00:01:53.889
and I can out the four up front,

00:01:53.889 --> 00:01:58.854
this is equal to four times
one half, four times one half,

00:02:00.492 --> 00:02:03.655
times our spring
constant, times d squared,

00:02:03.655 --> 00:02:06.888
which is equal to four
times the potential energy

00:02:06.888 --> 00:02:09.904
when we just compress the spring by d.

00:02:09.904 --> 00:02:11.772
So we already see a little
bit of what we talked about

00:02:11.772 --> 00:02:14.888
in part b, you compress
your spring twice as much,

00:02:14.888 --> 00:02:18.172
you're going to have four
times the potential energy,

00:02:18.172 --> 00:02:20.551
because the potential energy
doesn't grow proportionately

00:02:20.551 --> 00:02:24.004
with how much you compress
it, it grows with the square

00:02:24.004 --> 00:02:26.855
of how much you compress it.

00:02:26.855 --> 00:02:30.738
Alright, now let's think
about kinetic energy

00:02:32.799 --> 00:02:37.546
Kinetic energy when x is equal to zero,

00:02:41.682 --> 00:02:44.696
so right when the spring,
when we lose contact

00:02:44.696 --> 00:02:46.447
with the spring, the
spring is no longer pushing

00:02:46.447 --> 00:02:50.114
on the block, well our
kinetic energy is going to be

00:02:50.114 --> 00:02:53.647
equal to what our potential
energy was when the spring

00:02:53.647 --> 00:02:55.982
was actually compressed.

00:02:55.982 --> 00:02:58.447
Another way of thinking about
it, all that potential energy

00:02:58.447 --> 00:03:00.914
has now been turned into kinetic energy.

00:03:00.914 --> 00:03:02.531
Now what about over here?

00:03:02.531 --> 00:03:05.381
Well, the kinetic energy in this scenario,

00:03:05.381 --> 00:03:08.349
like we just saw before,
that's gonna be equal to the

00:03:08.349 --> 00:03:10.169
potential energy when the
spring was compressed.

00:03:10.169 --> 00:03:13.682
All of that potential energy
gets turned into kinetic energy

00:03:13.682 --> 00:03:17.284
and this is equal to four
times u one, four times

00:03:17.284 --> 00:03:19.725
the potential energy in
scenario one, which is the same

00:03:19.725 --> 00:03:23.482
thing as four times, which
is equal to four times

00:03:23.482 --> 00:03:26.060
the kinetic energy in scenario one.

00:03:26.060 --> 00:03:28.373
So we have four times the kinetic energy.

00:03:28.373 --> 00:03:33.164
Four times kinetic energy,
kinetic, kinetic energy.

00:03:36.783 --> 00:03:41.435
So then we have stopping
distance, stopping,

00:03:42.545 --> 00:03:46.137
stopping distance.

00:03:47.021 --> 00:03:49.862
We know here this is three d and we know,

00:03:49.862 --> 00:03:53.829
and then we can say "What's
this?", this question mark.

00:03:53.829 --> 00:03:56.148
Well let's just think a
little bit about this.

00:03:56.148 --> 00:03:59.914
We know that if we have
that kinetic energy

00:03:59.914 --> 00:04:01.692
at x equals zero,

00:04:01.692 --> 00:04:06.575
so we know that k one plus
the work done by friction,

00:04:08.058 --> 00:04:10.834
so let me make it clear,
this right over here,

00:04:10.834 --> 00:04:15.118
that is work done by friction,
work done by friction,

00:04:16.703 --> 00:04:19.785
and it's gonna be negative work
cause the force of friction

00:04:19.785 --> 00:04:23.986
is acting in the direction
opposite of the change in x,

00:04:25.153 --> 00:04:29.202
so the kinetic energy plus
the work done by friction

00:04:29.202 --> 00:04:32.084
is going to be equal to zero.

00:04:32.084 --> 00:04:35.293
This work cancels out all of this energy.

00:04:35.293 --> 00:04:38.569
When we think about it, it's
turning it all into heat.

00:04:38.569 --> 00:04:41.120
And so let's think about what
the work done by friction

00:04:41.120 --> 00:04:42.335
is equal to.

00:04:42.335 --> 00:04:46.851
Well the work done by friction
is equal to, is equal to,

00:04:48.620 --> 00:04:53.536
the coefficient of friction
times the mass of the block,

00:04:53.536 --> 00:04:58.018
times the gravitational
field, times how far,

00:05:00.879 --> 00:05:03.253
over what distance that
force, this right over here

00:05:03.253 --> 00:05:05.600
is the force of friction,
times over what distance

00:05:05.600 --> 00:05:10.260
that force was applied, so times three d.

00:05:10.260 --> 00:05:12.428
And to be clear, this force is going in

00:05:12.428 --> 00:05:16.078
the opposite direction of our change in x,

00:05:16.078 --> 00:05:20.486
so because of that this
will be a negative,

00:05:20.486 --> 00:05:25.034
and so we can say, we can
say that the kinetic energy

00:05:25.910 --> 00:05:30.445
at x equals zero, and now I
can just write it as minus

00:05:30.445 --> 00:05:33.761
mu, the coefficient of
friction, times mass, times

00:05:33.761 --> 00:05:38.515
the gravitational field, times
three d is equal to zero.

00:05:38.515 --> 00:05:41.053
We can add this to both
sides and we can get

00:05:41.053 --> 00:05:45.806
k one is equal to mu times
m times g times three d,

00:05:47.650 --> 00:05:49.902
and if you wanted to
solve for distance here,

00:05:49.902 --> 00:05:53.366
you can divide both sides
by the force of friction.

00:05:53.366 --> 00:05:56.684
So divide both sides by mu
times m times g, and you get

00:05:56.684 --> 00:05:58.984
three d, and I'm just
swapping the sides here,

00:05:58.984 --> 00:06:02.368
is going to be equal to the
amount of kinetic energy we have

00:06:02.368 --> 00:06:06.866
right as x equals zero,
divided by mu times m times g

00:06:08.685 --> 00:06:11.840
and you can just view this
as the force of friction.

00:06:11.840 --> 00:06:13.333
The force, I'll just call it

00:06:13.333 --> 00:06:16.602
the force of friction right over there.

00:06:16.602 --> 00:06:18.518
So if you wanna figure
out your stopping distance

00:06:18.518 --> 00:06:20.268
you just figure out your kinetic energy,

00:06:20.268 --> 00:06:23.082
right when you, right at x equals zero,

00:06:23.082 --> 00:06:26.365
right when you start entering
into the frictiony part of

00:06:26.365 --> 00:06:29.402
your platform and then you divide that by

00:06:29.402 --> 00:06:31.226
the force of friction,
and that will give you

00:06:31.226 --> 00:06:32.685
your distance traveled.

00:06:32.685 --> 00:06:37.000
So the distance here, distance,
so I can just put some

00:06:39.082 --> 00:06:42.350
arrows right over here,
our distance is going to be

00:06:42.350 --> 00:06:46.632
equal to k two divided by the force of,

00:06:48.901 --> 00:06:50.809
the force of friction.

00:06:50.809 --> 00:06:54.050
Well k two is equal to four times k one,

00:06:54.050 --> 00:06:57.420
is equal to four times k one.

00:06:57.420 --> 00:06:59.854
and our force of friction
is going to be the same

00:06:59.854 --> 00:07:01.755
We have the same coefficient of friction,

00:07:01.755 --> 00:07:03.737
we have the same mass, we have the same

00:07:03.737 --> 00:07:07.937
gravitational field, so
divided by force of friction,

00:07:07.937 --> 00:07:12.303
and this we already know, k one
divided by force of friction

00:07:15.205 --> 00:07:19.838
is equal to three d, so this
is all going to be equal to

00:07:19.838 --> 00:07:24.534
four, this is going to
be four times three d,

00:07:26.074 --> 00:07:30.814
three d, which is equal to 12 d, 12 d.

00:07:31.807 --> 00:07:34.156
So this is all a
mathematical way of saying

00:07:34.156 --> 00:07:36.776
you compress it twice as
much, you're going to have

00:07:36.776 --> 00:07:38.687
four times the potential energy when your

00:07:38.687 --> 00:07:40.822
spring is compressed, which
means you're going to have

00:07:40.822 --> 00:07:44.139
four times the kinetic
energy at x equals zero,

00:07:44.139 --> 00:07:46.705
which means it is going to
take, you're going to have

00:07:46.705 --> 00:07:49.622
four times the stopping
distance, so instead of stopping

00:07:49.622 --> 00:07:53.822
at three d or in six d as
what the student proposed,

00:07:53.822 --> 00:07:58.822
you are now stopping at 12 d, so that is

00:07:58.856 --> 00:08:01.406
our stopping distance.

00:08:01.406 --> 00:08:03.838
Did we answer all of, yeah
we answered all of part c.

00:08:03.838 --> 00:08:06.572
Use quantitative reasoning,
including equations as needed,

00:08:06.572 --> 00:08:08.906
to develop an expression
for the new final position

00:08:08.906 --> 00:08:09.621
of the block.

00:08:09.621 --> 00:08:12.755
Express your answer in terms of d.

00:08:12.755 --> 00:08:15.068
Yep, feel good about that.


2015 AP Physics 1 free response 3b

WEBVTT
Kind: captions
Language: en

00:00:00.411 --> 00:00:02.801
- [Voiceover] The spring is
now compressed twice as much,

00:00:02.801 --> 00:00:04.741
to delta x equals 2D.

00:00:04.741 --> 00:00:07.249
A student is asked to predict
whether the final position

00:00:07.249 --> 00:00:11.612
of the block will be twice
as far at x equals 6D.

00:00:11.612 --> 00:00:14.807
The student reasons that since
the spring will be compressed

00:00:14.807 --> 00:00:18.338
twice as much as before, the
block will have more energy

00:00:18.338 --> 00:00:21.623
when it leaves the spring,
so it will slide farther

00:00:21.623 --> 00:00:26.024
along the track before stopping
at position x equals 6D.

00:00:26.024 --> 00:00:28.844
So, let's just think about
what the student is saying

00:00:28.844 --> 00:00:30.816
or what's being proposed here.

00:00:30.816 --> 00:00:34.259
So, in the first version, the
first scenario, we compressed

00:00:34.259 --> 00:00:37.227
the block, we compressed the spring by D.

00:00:37.227 --> 00:00:40.721
And then, the spring
accelerates the block.

00:00:40.721 --> 00:00:43.183
And then, right when we
get back to x equals zero,

00:00:43.183 --> 00:00:45.066
all of that potential
energy has been turned into

00:00:45.066 --> 00:00:46.162
kinetic energy.

00:00:46.162 --> 00:00:50.977
And then, the friction is acting

00:00:50.977 --> 00:00:53.247
against the motion of the block,

00:00:53.247 --> 00:00:56.794
so you can view it as it's
providing negative work.

00:00:56.794 --> 00:01:01.717
The direction of the force is
opposite to the change in x.

00:01:01.717 --> 00:01:05.957
And the negative work eventually
causes the block to stop.

00:01:05.957 --> 00:01:09.961
And all of that kinetic energy
has now turned into heat.

00:01:09.961 --> 00:01:12.292
And so, the block goes 3D.

00:01:12.292 --> 00:01:15.397
Now, this new scenario, we
could call that scenario two,

00:01:15.397 --> 00:01:19.018
we are going to compress
the spring twice as far.

00:01:19.018 --> 00:01:22.826
So, now we're gonna compress
the spring twice as far.

00:01:22.826 --> 00:01:25.160
So, we're gonna compress it by 2D.

00:01:25.160 --> 00:01:27.758
So, this is x equals negative 2D here.

00:01:27.758 --> 00:01:30.140
And what's being said,
or what's being proposed,

00:01:30.140 --> 00:01:33.345
by the student is alright, if
we compress it twice as far,

00:01:33.345 --> 00:01:35.715
all of this potential
energy is then going to be,

00:01:35.715 --> 00:01:38.418
we're definitely going to have
more potential energy here

00:01:38.418 --> 00:01:42.006
because it takes more work to
compress the spring that far.

00:01:42.006 --> 00:01:43.845
And then, all of that more
potential energy is gonna

00:01:43.845 --> 00:01:46.360
be converted to more kinetic
energy once we get back

00:01:46.360 --> 00:01:47.985
to x equals zero.

00:01:47.985 --> 00:01:50.284
And so, not only will it go
further, but they're saying

00:01:50.284 --> 00:01:52.861
it'll go exactly twice as far.

00:01:52.861 --> 00:01:55.984
So, we are going to go,
instead of going to 3D, we are

00:01:55.984 --> 00:01:59.259
now going to go to 6D.

00:02:00.279 --> 00:02:01.580
Now, let's read.

00:02:01.580 --> 00:02:04.065
Let's see what the questions are here.

00:02:04.065 --> 00:02:06.376
And actually, I'm gonna put
a question mark here since

00:02:06.376 --> 00:02:09.506
I'm not sure if that is exactly right.

00:02:10.596 --> 00:02:14.500
So, part (b) i., let me do this.

00:02:15.649 --> 00:02:18.690
So, we're in part (b) i.

00:02:18.690 --> 00:02:20.908
It says which aspects of the
student's reasoning, if any,

00:02:20.908 --> 00:02:21.613
are correct.

00:02:21.613 --> 00:02:23.416
Explain how you arrived at your answer.

00:02:23.416 --> 00:02:25.191
And then, part two says which
aspects of the student's

00:02:25.191 --> 00:02:26.574
reasoning, if any, are incorrect.

00:02:26.574 --> 00:02:28.291
Explain how you arrived at your answer.

00:02:28.291 --> 00:02:32.297
So, the student is correct that two times,

00:02:32.297 --> 00:02:33.621
so compressing more,

00:02:34.655 --> 00:02:38.607
compressing spring more,

00:02:39.886 --> 00:02:44.822
spring more, will result

00:02:46.182 --> 00:02:50.367
in more energy when the
block leaves the spring,

00:02:50.367 --> 00:02:54.926
result in more energy

00:02:56.396 --> 00:03:00.336
when block leaves the spring,

00:03:00.336 --> 00:03:04.436
block leaves spring,

00:03:07.566 --> 00:03:09.486
which will result in the block

00:03:09.486 --> 00:03:14.442
going further, which will result,

00:03:16.990 --> 00:03:19.254
or the block going farther I should say,

00:03:19.254 --> 00:03:22.276
which will result in
longer stopping distance,

00:03:23.476 --> 00:03:27.933
which will result in longer stopping

00:03:29.483 --> 00:03:32.703
stopping distance.

00:03:33.803 --> 00:03:35.651
Now, part two.

00:03:36.711 --> 00:03:37.993
Part two, here.

00:03:37.993 --> 00:03:42.091
Which aspect of the
student's reasoning, if any,

00:03:42.091 --> 00:03:43.809
are incorrect.

00:03:43.809 --> 00:03:46.786
Explain how you arrive at your answer.

00:03:46.786 --> 00:03:51.499
Well, two times I could
say, let me say compressing,

00:03:52.759 --> 00:03:57.606
compressing twice as much,

00:03:59.566 --> 00:04:03.276
twice as much, does not result

00:04:03.276 --> 00:04:05.771
in exactly twice the stopping distance,

00:04:05.771 --> 00:04:10.643
does not result in

00:04:10.643 --> 00:04:14.033
twice the stopping distance,

00:04:15.213 --> 00:04:18.902
the stopping distance.

00:04:18.902 --> 00:04:22.252
And we can explain more if we like.

00:04:22.252 --> 00:04:26.542
We know that potential
energy is equal to 1/2 times

00:04:26.542 --> 00:04:31.351
the spring constant times how
much we compress, squared.

00:04:32.421 --> 00:04:35.581
So, we could say that energy,

00:04:35.581 --> 00:04:39.221
energy grows

00:04:40.351 --> 00:04:43.091
with the square,

00:04:44.521 --> 00:04:46.271
with the square,

00:04:46.271 --> 00:04:49.543
of compression of how much

00:04:49.543 --> 00:04:51.102
we compress it.

00:04:51.102 --> 00:04:55.132
of how much

00:04:55.132 --> 00:04:57.812
we compress.

00:04:59.702 --> 00:05:02.977
So, two times the compression.

00:05:02.977 --> 00:05:04.607
I'm gonna say two times.

00:05:04.607 --> 00:05:07.709
I'll write it out, two times compression

00:05:10.079 --> 00:05:13.341
will result in four times

00:05:14.491 --> 00:05:15.751
the energy.

00:05:17.351 --> 00:05:18.554
Energy.

00:05:18.554 --> 00:05:21.740
And this will result in four
times the stopping distance,

00:05:22.760 --> 00:05:27.680
four times stopping distance,

00:05:27.680 --> 00:05:30.690
four times stopping,

00:05:32.400 --> 00:05:36.200
stopping, distance.

00:05:36.200 --> 00:05:38.724
I think that it does a decent
job of explaining where

00:05:38.724 --> 00:05:41.105
the student is correct, where
their reasoning is correct,

00:05:41.105 --> 00:05:42.859
and where it is incorrect.


2015 AP Physics 1 free response 3a

WEBVTT
Kind: captions
Language: en

00:00:00.155 --> 00:00:01.927
- [Voiceover] A block
is initially at position

00:00:01.927 --> 00:00:03.270
x = zero,

00:00:03.270 --> 00:00:05.183
and in contact with an uncompressed spring

00:00:05.183 --> 00:00:06.798
of negligible mass.

00:00:06.798 --> 00:00:08.633
The block is pushed back
along a frictionless

00:00:08.633 --> 00:00:10.929
surface from position x = zero

00:00:10.929 --> 00:00:13.368
to x = -D, as shown above,

00:00:13.368 --> 00:00:15.237
compressing the spring by an amount

00:00:15.237 --> 00:00:17.768
delta x = D.

00:00:17.768 --> 00:00:21.402
So, the block starts here,
and it's just in contact

00:00:21.402 --> 00:00:22.944
with the spring, so it's initially,

00:00:22.944 --> 00:00:24.583
the spring is uncompressed.

00:00:24.583 --> 00:00:26.383
And it's just touching the block.

00:00:26.383 --> 00:00:28.249
And then we start to compress the spring

00:00:28.249 --> 00:00:30.158
by pushing the block to the left,

00:00:30.158 --> 00:00:32.537
and we compress it by an amount, D.

00:00:32.537 --> 00:00:35.479
They tell us that, right
there, delta x is = to D,

00:00:35.479 --> 00:00:37.145
so we compress,

00:00:37.145 --> 00:00:40.699
we move this block back
over to the left by D,

00:00:40.699 --> 00:00:43.276
that compresses the spring by D.

00:00:43.276 --> 00:00:46.202
The block is then released at x = zero,

00:00:46.202 --> 00:00:47.952
the block enters a rough part of the track

00:00:47.952 --> 00:00:49.706
and eventually comes to rest at position

00:00:49.706 --> 00:00:51.183
x = 3D.

00:00:51.183 --> 00:00:52.440
So when we compress the spring,

00:00:52.440 --> 00:00:54.798
we're actually doing to
work to compress the spring,

00:00:54.798 --> 00:00:58.217
so that work, that energy
from the, or the work

00:00:58.217 --> 00:01:00.589
we're doing, gets stored
as potential energy

00:01:00.589 --> 00:01:02.141
in the spring-block system.

00:01:02.141 --> 00:01:04.905
And then when we let go,
that potential energy is

00:01:04.905 --> 00:01:07.433
going to be converted to kinetic energy,

00:01:07.433 --> 00:01:09.576
and that block is going to be accelerated

00:01:09.576 --> 00:01:11.763
all the way until we get back to x = zero,

00:01:11.763 --> 00:01:13.567
then the spring is back to uncompressed,

00:01:13.567 --> 00:01:15.324
so it's not gonna keep
pushing on the block

00:01:15.324 --> 00:01:16.664
after that point.

00:01:16.664 --> 00:01:18.870
And then the block's going
to have this kinetic energy

00:01:18.870 --> 00:01:21.675
and if there was no friction
in this gray part here,

00:01:21.675 --> 00:01:23.116
it would just keep on going forever.

00:01:23.116 --> 00:01:24.689
And if there's no air
resistance, and we're assuming

00:01:24.689 --> 00:01:28.027
no air resistance for
this, for this problem,

00:01:28.027 --> 00:01:29.962
but since there is
friction, it's just going to

00:01:29.962 --> 00:01:32.880
decelerate it at a constant rate.

00:01:32.880 --> 00:01:35.529
You're going to have a
constant force of friction

00:01:35.529 --> 00:01:39.602
being applied to this block.

00:01:39.602 --> 00:01:41.952
So, let's see, they say, they tell us

00:01:41.952 --> 00:01:43.983
that it's going to come to rest at x = 3D,

00:01:43.983 --> 00:01:45.915
the coefficient of kinetic
friction between the block

00:01:45.915 --> 00:01:47.961
and the rough track is mu.

00:01:47.961 --> 00:01:50.502
Alright, on the axes
below, sketch and label

00:01:50.502 --> 00:01:52.418
graphs of the following two quantities

00:01:52.418 --> 00:01:54.495
as a function of the position of the block

00:01:54.495 --> 00:01:57.675
between x = negative D and x = 3D.

00:01:57.675 --> 00:02:00.972
You do not need to calculate
values for the vertical axis

00:02:00.972 --> 00:02:02.577
but the same vertical scale should be used

00:02:02.577 --> 00:02:04.083
for both quantities.

00:02:04.083 --> 00:02:06.009
So they have the kinetic
energy of the block

00:02:06.009 --> 00:02:10.246
and the potential energy
of the block-spring system.

00:02:10.246 --> 00:02:13.506
So let's first focus on
the potential energy, U,

00:02:13.506 --> 00:02:15.185
because when we start
the first part of this,

00:02:15.185 --> 00:02:16.366
when we're compressing the spring,

00:02:16.366 --> 00:02:18.757
that's when we're starting
to put potential energy

00:02:18.757 --> 00:02:20.848
into this spring-block system.

00:02:20.848 --> 00:02:22.845
So you have to think about
what is the potential energy

00:02:22.845 --> 00:02:25.492
of a compressed spring?

00:02:25.492 --> 00:02:27.830
Well, the potential energy

00:02:27.830 --> 00:02:29.241
the potential energy

00:02:29.241 --> 00:02:33.986
is equal to one-half
times the spring constant

00:02:33.986 --> 00:02:38.619
times how much you compress
the spring squared.

00:02:38.619 --> 00:02:40.661
So if we wanna say delta x is how much you

00:02:40.661 --> 00:02:43.980
compress the spring, that squared.

00:02:43.980 --> 00:02:45.332
Now, if what I just wrote is

00:02:45.332 --> 00:02:47.493
completely unfamiliar to you,

00:02:47.493 --> 00:02:50.075
I encourage you to watch
the videos on Khan Academy,

00:02:50.075 --> 00:02:52.323
the potential energy of
a compressed spring or

00:02:52.323 --> 00:02:54.518
the work necessary to compress a spring,

00:02:54.518 --> 00:02:56.155
cause the work necessary
to compress the spring

00:02:56.155 --> 00:02:57.457
that's going to be the potential energy

00:02:57.457 --> 00:03:00.076
that you're essentially
putting into that system.

00:03:00.076 --> 00:03:04.326
And so, for this, as we
compress the spring to D,

00:03:04.326 --> 00:03:06.301
you are, you're going to end up with

00:03:06.301 --> 00:03:11.249
a potential energy of one-half
times the spring constant

00:03:11.249 --> 00:03:14.352
x our change in x is D,

00:03:14.352 --> 00:03:15.656
our change in x is D.

00:03:15.656 --> 00:03:19.950
x D, x D squared.

00:03:19.950 --> 00:03:22.725
So let's plot that on
this right over here.

00:03:22.725 --> 00:03:23.503
So right,

00:03:23.503 --> 00:03:24.641
whoops,

00:03:24.641 --> 00:03:28.149
right when we are at x = zero

00:03:28.149 --> 00:03:30.504
there's no potential energy in our system,

00:03:30.504 --> 00:03:31.917
but then we start to compress it,

00:03:31.917 --> 00:03:33.798
and when we get to x = D,

00:03:33.798 --> 00:03:36.212
we're going to have a potential energy

00:03:36.212 --> 00:03:40.760
of one-half times the spring
constant times D squared.

00:03:40.760 --> 00:03:43.231
So let's just say this, right over here,

00:03:43.231 --> 00:03:45.225
let's say that over there,

00:03:45.225 --> 00:03:46.816
actually let me do a,

00:03:46.816 --> 00:03:48.451
let's see that one is,

00:03:48.451 --> 00:03:49.529
actually I'll do it over here so

00:03:49.529 --> 00:03:52.141
it'll be useful for me later on.

00:03:52.141 --> 00:03:55.336
So, let's say that this,
right over here, is one-half

00:03:55.336 --> 00:03:59.585
times our spring constant times D squared.

00:03:59.585 --> 00:04:01.942
So this is what our potential
energy's going to be like

00:04:01.942 --> 00:04:04.276
once we've compressed the spring by D.

00:04:04.276 --> 00:04:06.516
And it's not going to be a

00:04:06.516 --> 00:04:10.289
linear relationship,
remember the potential energy

00:04:10.289 --> 00:04:12.537
potential energy is
equal to one-half times

00:04:12.537 --> 00:04:14.552
the spring constant,

00:04:14.552 --> 00:04:17.834
times the spring constant,
times how much you've

00:04:17.834 --> 00:04:20.572
compressed the spring squared.

00:04:20.572 --> 00:04:23.780
So, the potential energy
increases as a sqaure

00:04:23.780 --> 00:04:25.938
of how much we've compressed the spring.

00:04:25.938 --> 00:04:26.996
So when we've compressed the spring

00:04:26.996 --> 00:04:28.681
half as much, we're going
to have one-fourth of

00:04:28.681 --> 00:04:30.643
the potential energy.

00:04:30.643 --> 00:04:32.550
So it's going to look
like this, it's gonna be

00:04:32.550 --> 00:04:35.008
you can view it as the
left side of a parabola.

00:04:35.008 --> 00:04:38.678
So it's going to, going to look something,

00:04:38.678 --> 00:04:41.118
something like this.

00:04:41.118 --> 00:04:43.399
So that's the potential energy.

00:04:43.399 --> 00:04:45.957
Now, when you're in this
point, when the thing is

00:04:45.957 --> 00:04:49.621
fully compressed, and then
you let go, what happens?

00:04:49.621 --> 00:04:53.307
Well that potential energy is
turned into kinetic energy,

00:04:53.307 --> 00:04:57.214
so as the spring, as the
spring accelerates the block,

00:04:57.214 --> 00:04:59.291
you're gonna go down this
potential energy curve,

00:04:59.291 --> 00:05:01.259
as you go to the right, but then, it gets

00:05:01.259 --> 00:05:02.800
converted to kinetic energy.

00:05:02.800 --> 00:05:05.136
So the potential energy
plus the kinetic energy

00:05:05.136 --> 00:05:08.006
needs to be constant, at
least over this period from

00:05:08.006 --> 00:05:10.943
x = negative D to x = zero.

00:05:10.943 --> 00:05:14.285
So the kinetic energy starts off at zero,

00:05:14.285 --> 00:05:15.328
it's stationary,

00:05:15.328 --> 00:05:18.968
but then, it starts, the block
starts getting accelerated.

00:05:18.968 --> 00:05:20.095
It starts getting accelerated.

00:05:20.095 --> 00:05:23.708
And the sum, the sum of these two things

00:05:23.708 --> 00:05:27.069
needs to be equal to one-half
times our spring constant

00:05:27.069 --> 00:05:28.811
times D squared.

00:05:28.811 --> 00:05:30.643
And so you can see if you,

00:05:30.643 --> 00:05:32.543
if you were to add these two curves

00:05:32.543 --> 00:05:35.240
at any position, you are going, their sum

00:05:35.240 --> 00:05:38.450
is going to sum up to this value.

00:05:38.450 --> 00:05:40.556
And so right when you
get back to x = zero,

00:05:40.556 --> 00:05:43.915
all of that potential energy
has been converted into

00:05:43.915 --> 00:05:45.376
kinetic energy.

00:05:45.376 --> 00:05:47.959
And then that kinetic
energy, we would stay at that

00:05:47.959 --> 00:05:50.225
high kinetic energy if
there was no friction

00:05:50.225 --> 00:05:51.560
or no air resistance.

00:05:51.560 --> 00:05:54.002
But we know that the
block comes to a rest at

00:05:54.002 --> 00:05:57.191
x is = to 3D.

00:05:57.191 --> 00:05:59.280
So all the kinetic energy
is gone at that point,

00:05:59.280 --> 00:06:01.370
and you might say well, what's
that getting converted into?

00:06:01.370 --> 00:06:04.215
Well, it's gonna get
converted into, into heat,

00:06:04.215 --> 00:06:05.496
due to the friction.

00:06:05.496 --> 00:06:07.357
So that's where, ya know, energy cannot be

00:06:07.357 --> 00:06:09.943
cannot be created out of thin
air or lost into thin air,

00:06:09.943 --> 00:06:12.609
it's converted from one form to another.

00:06:12.609 --> 00:06:13.693
And so the question is,

00:06:13.693 --> 00:06:15.012
what type of a curve is this?

00:06:15.012 --> 00:06:16.826
Do we just connect these with a line?

00:06:16.826 --> 00:06:18.696
Or is it some type of a curve?

00:06:18.696 --> 00:06:20.060
And the key realization is:

00:06:20.060 --> 00:06:22.584
is that you have a
constant force of friction

00:06:22.584 --> 00:06:25.742
the entire time that the
block is being slowed down,

00:06:25.742 --> 00:06:27.360
the coefficient of
friction doesn't change,

00:06:27.360 --> 00:06:28.960
so the force of friction,
and the mass of the block

00:06:28.960 --> 00:06:31.015
isn't changing, so the force of friction's

00:06:31.015 --> 00:06:32.319
going to be the same.

00:06:32.319 --> 00:06:34.830
And it's acting against
the motion of the block.

00:06:34.830 --> 00:06:36.927
So you can, you can view
the friction as essentially

00:06:36.927 --> 00:06:38.764
doing this negative work,

00:06:38.764 --> 00:06:40.971
and so it's sapping the energy away,

00:06:40.971 --> 00:06:42.642
if you think about it
relative to distance,

00:06:42.642 --> 00:06:44.930
in a given amount of
distance, it's sapping away

00:06:44.930 --> 00:06:46.897
the same amount of energy, it's doing that

00:06:46.897 --> 00:06:50.319
same amount of negative work.

00:06:50.319 --> 00:06:54.128
And so, this is going to
decrease at a linear rate.

00:06:54.128 --> 00:06:56.336
So, let me draw that.

00:06:56.336 --> 00:07:00.040
So it's gonna be a linear decrease,

00:07:00.040 --> 00:07:01.154
just like that.

00:07:01.154 --> 00:07:02.799
And the key thing to remind yourself is:

00:07:02.799 --> 00:07:06.740
is this is a plot of
energy versus position,

00:07:06.740 --> 00:07:10.000
not velocity versus position
or velocity versus time,

00:07:10.000 --> 00:07:11.977
or energy versus time.

00:07:11.977 --> 00:07:15.195
This is energy versus position,
and that's what gives us

00:07:15.195 --> 00:07:19.170
this linear relationship right over here.

00:07:19.170 --> 00:07:23.467
So, we have the kinetic
energy, k, of the block.

00:07:23.467 --> 00:07:24.766
That's what I did in magenta,

00:07:24.766 --> 00:07:27.248
so this is the kinetic energy.

00:07:27.248 --> 00:07:29.403
Kinetic,

00:07:29.403 --> 00:07:32.598
kinetic energy,

00:07:32.598 --> 00:07:35.184
and in blue, just to make
sure I label it right,

00:07:35.184 --> 00:07:37.740
this is the potential energy,

00:07:37.740 --> 00:07:40.133
potential,

00:07:40.133 --> 00:07:45.026
potential energy.


2015 AP Physics 1 free response 5

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.502
- [Voiceover] The figure
above shows a string

00:00:02.502 --> 00:00:05.038
with one end attached to an oscillator

00:00:05.038 --> 00:00:07.607
and the other end
attached to a block there.

00:00:07.607 --> 00:00:08.708
There's our block.

00:00:08.708 --> 00:00:11.745
The string passes over a
massless pulley that turns

00:00:11.745 --> 00:00:13.079
with negligible friction.

00:00:13.079 --> 00:00:15.081
There's our massless pulley that turns

00:00:15.081 --> 00:00:16.722
with negligible friction.

00:00:16.722 --> 00:00:20.887
Four such strings, A, B, C,
and D are set up side-by-side

00:00:20.887 --> 00:00:23.757
as shown in the figure
in the diagram below.

00:00:23.757 --> 00:00:26.559
So this is a top view,
you can see oscillator.

00:00:26.559 --> 00:00:28.995
This is a top view of the
oscillator string pulley

00:00:28.995 --> 00:00:31.798
mass system, and we have four of them.

00:00:31.798 --> 00:00:34.601
Each oscillator is adjusted
to vibrate the string

00:00:34.601 --> 00:00:36.903
at its fundamental frequency f.

00:00:36.903 --> 00:00:38.905
So let's think about what
it, I'll keep reading

00:00:38.905 --> 00:00:41.908
then we'll think about what
fundamental frequency means.

00:00:41.908 --> 00:00:45.345
The distance between each
oscillator and the pulley L

00:00:45.345 --> 00:00:46.346
is the same.

00:00:46.346 --> 00:00:48.681
So the length between the
oscillator and the pulley

00:00:48.681 --> 00:00:52.519
is the same, and the mass
of each block is the same.

00:00:52.519 --> 00:00:55.355
So the mass is what's providing
the tension in the string.

00:00:55.355 --> 00:00:57.957
However, the fundamental
frequency of each string

00:00:57.957 --> 00:00:59.092
is different.

00:00:59.092 --> 00:01:01.094
So let's just first of all think about

00:01:01.094 --> 00:01:03.096
what the fundamental frequency is,

00:01:03.096 --> 00:01:05.098
and then let's think about
what makes them different.

00:01:05.098 --> 00:01:06.299
So the fundamental frequency,

00:01:06.299 --> 00:01:08.301
one way you could think about it is

00:01:08.301 --> 00:01:10.970
it's the lowest frequency
that is going to produce

00:01:10.970 --> 00:01:13.592
a standing wave in your string.

00:01:13.592 --> 00:01:16.702
So it's the frequency that
produces a standing wave

00:01:16.702 --> 00:01:18.522
that looks like this.

00:01:18.522 --> 00:01:23.522
It's a standing wave where the
string is half a wavelength.

00:01:25.923 --> 00:01:27.487
I guess there's two
ways to think about it.

00:01:27.487 --> 00:01:29.489
It's the lowest frequency we could produce

00:01:29.489 --> 00:01:31.491
the standing wave, or it's
the frequency at which

00:01:31.491 --> 00:01:34.627
you're producing the
wave, the standing wave,

00:01:34.627 --> 00:01:37.330
with the longest wavelength.

00:01:37.330 --> 00:01:39.332
So the string at the fundamental frequency

00:01:39.332 --> 00:01:41.334
is just going to go to, is gonna vibrate

00:01:41.334 --> 00:01:43.436
between those two positions.

00:01:43.436 --> 00:01:47.795
And you see here that the wavelength here

00:01:47.795 --> 00:01:49.404
is twice the length of the string.

00:01:49.404 --> 00:01:50.935
And if you want to see
that a little bit clearer,

00:01:50.935 --> 00:01:53.105
if I were to continue with this wave,

00:01:53.105 --> 00:01:55.064
I would have to go another
length of the string

00:01:55.064 --> 00:01:58.918
in order to complete one wavelength.

00:01:58.918 --> 00:01:59.957
Or another way to think about it,

00:01:59.957 --> 00:02:02.922
you're going up, down, and
then you're going down back.

00:02:02.922 --> 00:02:05.925
It's reflecting back off of this end here.

00:02:05.925 --> 00:02:09.229
And as we mentioned, essentially
what the mass is doing

00:02:09.229 --> 00:02:12.866
is providing the tension, the
force of gravity on this mass

00:02:12.866 --> 00:02:15.869
is providing the tension in this string.

00:02:15.869 --> 00:02:18.638
So the oscillators is vibrating
at the right frequency

00:02:18.638 --> 00:02:22.308
to produce this, the lowest
frequency where you can produce

00:02:22.308 --> 00:02:24.664
this standing wave.

00:02:24.664 --> 00:02:28.114
So let's answer the questions
now, and we have four

00:02:28.114 --> 00:02:31.551
of this set up and they all
have different frequencies.

00:02:31.551 --> 00:02:35.154
The equation for the velocity
v of a wave on a string

00:02:35.154 --> 00:02:38.491
is v is equal to the
square root of the tension

00:02:38.491 --> 00:02:41.294
of the string divided by
the mass of the string

00:02:41.294 --> 00:02:43.296
divided by the length of the string,

00:02:43.296 --> 00:02:45.298
where F sub T is tension of the string

00:02:45.298 --> 00:02:48.167
and m divided by L is
the mass per unit length,

00:02:48.167 --> 00:02:50.169
linear mass density of the string.

00:02:50.169 --> 00:02:51.533
And hopefully this makes sense.

00:02:51.533 --> 00:02:54.340
It makes sense that it's
going to be that if,

00:02:54.340 --> 00:02:57.043
if the tension increases, that
your velocity will increase,

00:02:57.043 --> 00:02:59.712
the tension, you could think
of the atoms of the string

00:02:59.712 --> 00:03:02.248
of how much they're pulling on each other.

00:03:02.248 --> 00:03:05.697
And so if there's higher tension, well,

00:03:05.697 --> 00:03:07.139
they're going to be able
to move each other better,

00:03:07.139 --> 00:03:09.216
or I guess you could say
accelerate each other better

00:03:09.216 --> 00:03:13.026
as the wave goes through the string.

00:03:13.026 --> 00:03:15.324
And also make sense that
the larger the mass,

00:03:15.324 --> 00:03:17.033
if you hold everything else equal,

00:03:17.033 --> 00:03:18.586
that you're gonna have a slower velocity.

00:03:18.586 --> 00:03:22.004
Mass, you could view it

00:03:22.004 --> 00:03:24.054
as a measure of inertia,
it's how hard it is

00:03:24.054 --> 00:03:25.538
to accelerate something.

00:03:25.538 --> 00:03:28.941
So if the string itself,
especially the mass

00:03:28.941 --> 00:03:33.268
per unit length, if there's a
lot of mass per unit length,

00:03:33.268 --> 00:03:34.910
actually, let me circle
that because that's actually

00:03:34.910 --> 00:03:36.401
the more interesting thing.

00:03:36.401 --> 00:03:39.337
If there's a lot of mass per unit length,

00:03:39.337 --> 00:03:41.654
it makes sense that for a
given amount of the string,

00:03:41.654 --> 00:03:44.757
it's gonna be harder to
accelerate it back and forth

00:03:44.757 --> 00:03:45.992
as you vibrate it.

00:03:45.992 --> 00:03:50.129
And so this part right over
here would be inversely related

00:03:50.129 --> 00:03:51.300
to the velocity.

00:03:51.300 --> 00:03:52.395
It's not proportional though.

00:03:52.395 --> 00:03:54.067
You have this square root here,

00:03:54.067 --> 00:03:55.708
but they're definitely,

00:03:55.708 --> 00:03:58.237
if the linear mass density increases,

00:03:58.237 --> 00:04:00.239
then you're gonna have a slower velocity.

00:04:00.239 --> 00:04:02.809
And if your tension increases,
you're going to have

00:04:02.809 --> 00:04:03.810
a higher velocity.

00:04:03.810 --> 00:04:06.446
So hopefully this makes
some intuitive sense.

00:04:06.446 --> 00:04:08.548
And they ask, what is the
difference about the four string

00:04:08.548 --> 00:04:11.217
shown above that would
result in having different

00:04:11.217 --> 00:04:13.119
fundamental frequencies?

00:04:13.119 --> 00:04:15.421
Explain how you arrive at your answer.

00:04:15.421 --> 00:04:17.423
And then part b is
student graphs frequency

00:04:17.423 --> 00:04:20.994
is a function of the inverse
of the linear mass density.

00:04:20.994 --> 00:04:22.729
Will the graph be linear?

00:04:22.729 --> 00:04:24.864
Explain how you arrived at your answer.

00:04:24.864 --> 00:04:27.266
All right, let's answer each of these.

00:04:27.266 --> 00:04:31.738
So a, part a, what is different
about the four strings

00:04:31.738 --> 00:04:33.973
because they all have different
fundamental frequencies?

00:04:33.973 --> 00:04:36.909
So the fundamental frequency,

00:04:36.909 --> 00:04:40.079
let's just go back to
what we know about waves,

00:04:40.079 --> 00:04:44.283
that the velocity of a wave
is equal to the frequency

00:04:44.283 --> 00:04:48.187
times the wavelength of the wave.

00:04:48.187 --> 00:04:51.257
Or you could say, you could
divide both sides by lambda,

00:04:51.257 --> 00:04:53.259
you could say that the frequency of a wave

00:04:53.259 --> 00:04:57.764
is equal to the velocity
over the velocity over

00:04:57.764 --> 00:04:58.998
the wavelength.

00:04:58.998 --> 00:05:02.114
So if we're talking about
the fundamental frequency,

00:05:02.114 --> 00:05:04.937
if we're talking about
the fundamental frequency,

00:05:04.937 --> 00:05:07.696
funda, let me just,

00:05:07.696 --> 00:05:09.809
let me write frequency and
then let me write fundamental

00:05:09.809 --> 00:05:11.144
real small here.

00:05:11.144 --> 00:05:14.514
Fundamental, the fundamental frequency,

00:05:14.514 --> 00:05:17.917
is going to be the velocity of our waves

00:05:17.917 --> 00:05:21.054
divided by the wavelength is
going to be twice the length

00:05:21.054 --> 00:05:24.524
of our string, divided by two L.

00:05:24.524 --> 00:05:27.527
And if you look at the
expression that they gave us

00:05:27.527 --> 00:05:30.463
for the velocity of
the wave on the string,

00:05:30.463 --> 00:05:32.765
well, this is going to be equal to

00:05:32.765 --> 00:05:36.836
the square root of the
tension in the string

00:05:36.836 --> 00:05:41.836
divided by, divided by
the linear mass density.

00:05:42.241 --> 00:05:44.243
Divided by the linear mass density.

00:05:44.243 --> 00:05:47.780
And all of that is going to be over two L.

00:05:47.780 --> 00:05:49.949
Now all of them have different
fundamental frequencies,

00:05:49.949 --> 00:05:51.951
but let's think about
what's different over here.

00:05:51.951 --> 00:05:54.587
They all have the same tension.

00:05:54.587 --> 00:05:56.689
They all have the same tension.

00:05:56.689 --> 00:05:57.824
How do I know that?

00:05:57.824 --> 00:05:59.826
Well, what's causing the
tension is the masses

00:05:59.826 --> 00:06:01.797
hanging over the pulleys.

00:06:01.797 --> 00:06:03.616
So the weight of those masses.

00:06:03.616 --> 00:06:05.535
So that's all going to be
the same for all of them,

00:06:05.535 --> 00:06:07.833
and they all have the same length.

00:06:07.833 --> 00:06:10.193
They all have the same length.

00:06:10.193 --> 00:06:12.004
So these are all the same.

00:06:12.004 --> 00:06:13.973
So the only way that you're
going to have different

00:06:13.973 --> 00:06:18.010
fundamental frequencies is
if you have different masses.

00:06:18.010 --> 00:06:19.679
So different masses.

00:06:19.679 --> 00:06:22.415
So that has to be different.

00:06:22.415 --> 00:06:24.650
Different.

00:06:24.650 --> 00:06:27.220
So to answer their question,

00:06:27.220 --> 00:06:29.455
the strings must have different mass,

00:06:29.455 --> 00:06:32.091
well, they would have different
linear mass densities,

00:06:32.091 --> 00:06:33.181
but since they're all the same length,

00:06:33.181 --> 00:06:35.035
they would also have different masses.

00:06:35.035 --> 00:06:37.163
So let me write this down.

00:06:37.163 --> 00:06:41.467
Strings, strings must

00:06:42.667 --> 00:06:45.316
have different,

00:06:47.073 --> 00:06:49.610
different masses

00:06:51.277 --> 00:06:53.379
and mass densities,

00:06:53.379 --> 00:06:56.135
and mass densities,

00:06:57.383 --> 00:06:59.786
densities, since

00:07:02.288 --> 00:07:05.400
all other variables

00:07:07.293 --> 00:07:10.241
driving, driving

00:07:12.064 --> 00:07:14.400
fundamental frequency are the same,

00:07:14.400 --> 00:07:18.371
fundamental frequency

00:07:20.840 --> 00:07:23.342
are the same,

00:07:23.342 --> 00:07:27.280
are the same.

00:07:27.280 --> 00:07:29.745
All right, let's tackle part b now.

00:07:30.883 --> 00:07:33.820
A student graphs frequency as a function

00:07:33.820 --> 00:07:37.256
of the inverse of linear mass density.

00:07:37.256 --> 00:07:39.458
Will the graph be linear?

00:07:39.458 --> 00:07:41.928
Explain how you arrived at your answer.

00:07:41.928 --> 00:07:44.063
So student graphs frequency.

00:07:44.063 --> 00:07:45.965
Let me underline this.

00:07:45.965 --> 00:07:48.835
They're graphing frequency as a function

00:07:48.835 --> 00:07:51.871
of linear mass density.

00:07:51.871 --> 00:07:54.073
So we actually can write this down.

00:07:54.073 --> 00:07:56.242
If we wanted to write frequency

00:07:56.242 --> 00:07:58.611
as a function of linear mass densities,

00:07:58.611 --> 00:08:01.914
so we could write as a
function of m over L,

00:08:01.914 --> 00:08:04.016
well, this is going to be equal to,

00:08:04.016 --> 00:08:05.451
is going to be equal to,

00:08:05.451 --> 00:08:07.653
we could rewrite this expression,

00:08:07.653 --> 00:08:09.655
actually, we could just
leave it like this.

00:08:09.655 --> 00:08:12.225
This is the same thing as one over two L

00:08:12.225 --> 00:08:15.661
times the square root of the tension

00:08:15.661 --> 00:08:19.866
divided by the linear mass density.

00:08:19.866 --> 00:08:21.868
Or you can do this as being equal to,

00:08:21.868 --> 00:08:25.371
you could say this is a square root of

00:08:25.371 --> 00:08:28.007
the tension over two L,

00:08:28.007 --> 00:08:30.009
and I'm putting all of
this separate because

00:08:30.009 --> 00:08:32.477
we're doing it as a function
of our linear mass density.

00:08:32.477 --> 00:08:36.716
So we can assume that all of
this is going to be a constant.

00:08:36.716 --> 00:08:39.751
And then times the square root

00:08:39.751 --> 00:08:43.990
of one over the linear mass density.

00:08:44.860 --> 00:08:48.928
So if you're plotting, if
you're plotting frequency

00:08:48.928 --> 00:08:51.397
as a function of this,

00:08:51.397 --> 00:08:53.933
it's not going to be,
the graph is definitely

00:08:53.933 --> 00:08:56.168
not going to be linear.

00:08:56.168 --> 00:08:58.404
You see here, one, I have
the reciprocal of it,

00:08:58.404 --> 00:09:00.439
and then I take the square root of it.

00:09:00.439 --> 00:09:04.482
So let me write this down.

00:09:07.273 --> 00:09:12.273
This f or graph of f of two L,

00:09:12.396 --> 00:09:13.382
definitely not linear.

00:09:13.382 --> 00:09:15.012
Let me write it that way.

00:09:15.012 --> 00:09:19.428
F of m over L graph,

00:09:21.869 --> 00:09:25.833
definitely, definitely

00:09:26.784 --> 00:09:28.967
not linear.

00:09:30.355 --> 00:09:32.709
And you could point out
that it has a reciprocal

00:09:32.709 --> 00:09:34.033
and it's a square root.

00:09:34.033 --> 00:09:38.678
Involves, involves square root

00:09:38.678 --> 00:09:42.048
and inverse,

00:09:42.048 --> 00:09:45.351
or I could say and
reciprocal of the variable.

00:09:45.351 --> 00:09:49.165
And reciprocal, reciprocal

00:09:50.525 --> 00:09:52.858
of the linear mass density

00:09:52.858 --> 00:09:54.260
of m over L.

00:09:54.260 --> 00:09:55.561
So definitely not linear.

00:09:55.561 --> 00:09:58.364
All right, let's tackle part c.

00:09:58.364 --> 00:10:01.634
The frequency of the oscillator
connected to string D

00:10:01.634 --> 00:10:04.236
is changed so that the string vibrates

00:10:04.236 --> 00:10:06.405
in its second harmonic.

00:10:06.405 --> 00:10:09.075
On the side view of string D below,

00:10:09.075 --> 00:10:11.677
mark and label the points
on the string that have

00:10:11.677 --> 00:10:14.113
the greatest average vertical speed.

00:10:14.113 --> 00:10:16.115
So one way to think about
the fundamental frequency,

00:10:16.115 --> 00:10:17.116
that's our first harmonic.

00:10:17.116 --> 00:10:19.118
So if they're talking
about the first harmonic

00:10:19.118 --> 00:10:22.788
and the string is what I showed before,

00:10:22.788 --> 00:10:26.928
that's the lowest frequency
that produces a standing wave

00:10:26.928 --> 00:10:29.228
or it's the frequency
that produces the largest

00:10:29.228 --> 00:10:30.546
standing wave, I guess
you could say the one

00:10:30.546 --> 00:10:31.774
with the largest wavelength.

00:10:31.774 --> 00:10:33.168
And if it was a first harmonic,

00:10:33.168 --> 00:10:35.091
the part of the string that moves the most

00:10:35.091 --> 00:10:36.737
is going to be that center.

00:10:36.737 --> 00:10:39.538
But our second harmonic is
the next highest frequency

00:10:39.538 --> 00:10:41.807
that produces a standing wave,

00:10:41.807 --> 00:10:44.143
and that's going to be
a situation in which

00:10:44.143 --> 00:10:46.746
the wave, instead of having
a wavelength twice the length

00:10:46.746 --> 00:10:48.109
of the string, it's
gonna have a wavelength

00:10:48.109 --> 00:10:49.988
equal to the length of the string.

00:10:49.988 --> 00:10:53.285
So now, it's going to look like this.

00:10:53.285 --> 00:10:56.657
So it's going to vibrate between this,

00:10:56.657 --> 00:10:59.125
actually, let me draw it a
little bit neater than that.

00:10:59.125 --> 00:11:02.288
It's going to vibrate between,

00:11:03.429 --> 00:11:05.180
between this.

00:11:06.320 --> 00:11:09.335
And so

00:11:10.325 --> 00:11:13.636
it's gonna vibrate between that and this.

00:11:13.636 --> 00:11:15.508
And this right over here.

00:11:16.742 --> 00:11:19.578
So when you see this, this version of it,

00:11:19.578 --> 00:11:21.580
where now that we have
half the wavelength,

00:11:21.580 --> 00:11:25.120
the wavelength is exactly
the wavelength of,

00:11:25.120 --> 00:11:26.652
it's actually L this time,

00:11:26.652 --> 00:11:30.314
the part that moves the most is here.

00:11:30.314 --> 00:11:31.701
So that's going to move the most.

00:11:31.701 --> 00:11:33.259
And here.

00:11:33.259 --> 00:11:35.056
I didn't draw it perfectly.

00:11:35.056 --> 00:11:37.930
But one way to think
about it, it's exactly 1/4

00:11:37.930 --> 00:11:39.732
and 3/4 of the way.

00:11:39.732 --> 00:11:42.134
Exactly halfway is not
going to move as much,

00:11:42.134 --> 00:11:44.336
is not gonna move because
it's a standing wave now

00:11:44.336 --> 00:11:46.338
or it's gonna move very imperceptibly.

00:11:46.338 --> 00:11:49.208
These two places are where
you're gonna move the most

00:11:49.208 --> 00:11:53.145
at the first, or sorry,
at the second harmonic.

00:11:53.145 --> 00:11:56.816
The second harmonic being
the next highest frequency

00:11:56.816 --> 00:11:59.982
that produces a standing wave again.