Hi, my name is Madeleine and I’ve just finished
my second year of Engineering at Jesus College,
Cambridge.
I applied in 2012 and matriculated in 2013.
I’m going to go through 2 interview questions
which are taken from the website I want to
study Engineering.org which is a website which
has hundreds of engineering interview type
questions with worked through answers and
occasionally videos too.
The two questions that I’m going to do are
similar to the kind of questions that I got
during my interviews.
So hopefully this will help.
So the first question reads as follows.
On a clear day, you are on an airplane which
is 38,000 ft above the middle of Pacific Ocean.
Taking the radius of the Earth to be 6,400km,
what is the approximate distance between you
& the horizon of the Earth?
You are also given that 1 foot is equivalent
to 0.3048 meters.
So the first thing that I would do is convert
the 30000 feet into meters using the given
conversion.
So 38 000 ft times by 0.3084 meters is roughly,
using a calculator, 11.6km So now that you
have all of the figures in meters or km, you
can then draw a diagram of the earth with
the center here and you can say that the airplane
is hereish.
So now marking the distances on, you know
that this, the radius of the earth, is 6400km.
I’m just going to say all the distances
are in Km.
Then the distance from the plane to the Pacific
Ocean is, as we calculated here, 11.6kms.
So now we need to think about where the horizon
is.
So the horizon is the line of sight from where
you are in the airplane to the first point
you can see.
By definition or by intuition, you can say
that point has to be at right angles with
the radius of the earth because if you are
looking at this way and say that this is your
line of sight and this is with the horizon
and it’s essentially where your line is
horizontal with the circumference of the earth.
So if we then draw the radius of the earth
on to this point you know this has to be a
right angle and, so from then on, it’s essentially
a Pythagoras question.
So again this is the radius of the earth and
you are trying to find the approximate distance
between you and the horizon.
So if we call this x (that’s the distance
here).
So then if we redraw the triangle, we have
x here, 6400km here and, in total, 6411.6
here and so by Pythagoras which in full of
course is this and by rearranging this to
get x; as the result, you find the x, the
approximate distance between you and the horizon
of the earth is roughly 386km.
The second question which is I’m going to
go through goes as follows.
A rocket of mass m is to be launched from
the surface of a rogue planet with mass M
and radius R and no atmosphere.
By making reasonable assumptions about the
distance between the planet and any nearby
galaxies, find the escape velocity required
for the rocket to overcome the gravitational
field of the planet.
You might be wondering what the reasonable
assumptions mentioned in the questions might
mean.
And you just really need to think about what
the effect of other planets close by to this
planet might be.
So if there are planets close to the rogue
planet, it’s likely that their gravitational
field that have an effect on the motion of
the rocket.
Therefore, the assumption that you need to
make is the distance between this planet and
any nearby planets is very, very large and,
therefore, only the gravitational field of
the rogue planet is important in this question.
So for this question, I’ll go straight into
drawing a diagram as it might make it clearer
as to what you need to do to solve this problem.
Say this is the planet and we can mark on
here that this is the radius big R. Now if
we draw the rocket to be here at any moment
in time, we can label the distance from the
rocket to the center of the earth as little
r.
So this is just something that we can define.
Say in another given time, the rocket has
now moved.
So it’s got a little further and we are
going to say that the distance between this
instance and this instance is delta r (just
to symbolize a little distance).
So we know that as the rocket is moving, there
must be a force due to the gravitational field
of this planet acting on the rocket and this
force is going to be in this direction which
we can call big F and we know in this instance
it will also be acting obviously with a different
value which is given by the formula F equals
big G and then the mass of the planet which
is capital M, the mass of the body upon which
the force is acting which is the little m
over the distance between the two bodies which
we have to find as r2.
Now with kinetic energy questions, you often
immediately think of energy balancing equations.
So this might help in this problem.
One energy balance equation that we know is
that the work done is equal to force times
distance.
Although we don’t quite know how we are
going to get to kinetic energy through this,
it might be worth a try.
We know that the force on the rocket is going
to be given by the equation that we just wrote
down and if you don’t remember this equation
in the interview or you haven’t seen it
before just as an example in an interview
if you can’t think of the equation or you
really don’t know it; if you just state
it, say “I’m really sorry I don’t think
I can’t quite really remember the formula
of the equation” They will usually give
it to you as it will help you solve the question
and they just don’t want you to stop in
your tracks so they will help you if you forget
things that might be useful.
So yes force times this force times the little
distance.
So we are working out the work that’s done
for the rocket moving from here to here.
So we will do times delta r.
Now this here is just an equation for the
little amount of work done moving the rocket
from this position to this position which
is just an arbitrary small distance.
So to get the total amount of work that will
be needed to get the rocket from the surface
of the earth as specified in the question
all the way to outside the gravitational field
of the planet we will need to sum all these
little works done from bigger to infinity
which is where the gravitational field of
the planet will end.
Now if this isn’t an intuitive step and
you don’t get it in the interview, they
may again the interviewers may again help
you so that you might be able to proceed further
with the question.
So don’t panic.
Therefore the total work done which I’m
going to write as w will be equal to the integral
between big R (so the radius of the planet)
and infinity of this.
And now you can see it’s just an integral
but we need to calculate to get the work done.
So to do the integral, you can rewrite the
over r2 as r to the power of -2 which makes
it easier and then you can see that by adding
1, dividing by the new power you get minus
… r to -1 which you can put on the bottom
again between r to infinity.
Now this when you put the limits in, the first
limit you put in is infinity obviously dividing
by infinity is going to give you zero and
then the next step is you are doing is minus
and then inserting large R; so you end up
with a minus minus big G big M little m over
big R. Now this is just the total work done.
So I’ve just moved the result of this integral
up here to save space for the next bit of
the question.
As I have said in the beginning, when you
think of kinetic energy questions you may
think of work done and energy balance equations.
So now we have the total work needed to get
the rocket from here to outside the gravitational
field.
Through energy balance, you know that the
work done that is needed to do this must be
equal to the initial kinetic energy that the
rocket has when it’s at the surface of the
planet.
Therefore, we can write that the result of
our integral must be equal to half mv squared.
From now on, it’s just rearranging to find
the v which is the escape velocity, as specified
in the question.
So mv2 is 2GFm over big R; therefore, in the
end you get v as equal to 2GbigM/R as the
two ms cancel and the whole thing square rooted.
And this is the formula for the escape velocity.
So these were the two interview questions.
I hope you found them useful.
If you want to see anymore, go to the website
that I mentioned earlier, I want to study
Engineering.org.
But if I were to give any tips for the interview,
I would say try not to panic I know it’s
really hard and obviously you are going to
feel stressed.
But if you forget anything in a spark of moment,
if you misremember an equation or if you literally
can’t see where this question is going,
don’t be afraid to admit that.
The interviewers are there to help and I’m
sure teacher or whoever might have been telling
you that already.
You may not believe but it is true they will
try and help you through a question they won’t
just leave you in a alert they just want to
test you with things that you haven’t seen
before so maybe using equations that you might
have seen in Math and Physics for example
the gravitational force equation and then
use it in a way that you might not be familiar
with.
So they just want to see how well you pick
up new concepts or at least that’s the idea
that I got from my interview and speaking
to my interviewers who are now also my supervisors.
That is generally the thing that they are
trying to do or, at least in my college, that’s
what they are trying to do.
So try and not to panic and don’t be afraid
to admit if you don’t know something.
I quoted FM = ma in my interview and they
still let me in.
So don’t worry if you slip up.
Try and enjoy it these are some of the most
renowned academics in the engineering field
who will be interviewing you probably.
They really are there to try and test you
obviously but they will also help you through
it.
So they are not the enemy.
So hopefully that was useful and I wish you
all good luck.
