Force exerted by space debris on satellites Hypothetically, if space debris were to collide with the currently orbiting satellites, how much force would they exert, and how much damage would they make?
Will the satellites be able to withstand that much force, especially if they don't have Whipple shields?
Since space debris travel at tremendous velocities, I am guessing the force is pretty large too. How do you calculate the force? Is it a simple $\rm{F=m \cdot a}$ calculation?
The force depends on the details of the collision. Depending on how hard the materials involved are, and the angles and everything, it might be a larger force for a shorter time, or a shorter force for a larger time. 

What are relatively predictable is the impulse -- force times time, essentially (or the integral of force over time, if you want to be exact) and the energy released by the impact. For a small piece of debris these are determined by the mass and velocity of the debris with respect to the satellite. 

Relative velocities are typically a few km/s, so, 1 mg piece of debris (a paint flake or something like that) will deliver about $10^{-3} kg m/s$ of impulse, and about $10--100J$ of energy.  The impulse will change the orbit of the satellite (typical mass perhaps 1 ton) by very little. Perturbations from tides and other effects will be bigger. The energy is more of a concern -- depending on what it hits something may get hot, or have a hole made in it. 

A much larger piece of debris (say 1g -- a small screw) carries 1000 times the impulse and energy and may will wreck a satellite (although if it hits a solar panel or something it may just make a hole and go on through). If the satellite survived, then it the change to its orbit would be noticeable, but not a huge deal.