A block of mass 2 kg is initially at rest on a horizontal surface. At time , we begin pushing on it with a horizontal force that varies with time as , where 0.6 N/s . We stop pushing at time s [ for ].

Question

(a) First, assume the surface is frictionless. What is the magnitude of the final momentum of the block at s? (in kg m/s)



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(b) Let us now consider a new situation where the object is initially at rest on a rough surface. The coefficient of static friction is . What is the speed of the block at time s?. For simplicity, we take static and kinetic friction coefficients to be the same, and consider m/s .



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(c) What is the power provided by the force at time s (in Watts) in the case where there is friction (part (b)) ?

Answer 1

The first part is easy: change in momentum is impulse, which you can find by integrating F from 0 to your time.

Now, what about b)?

Answer 2

The same goes for part b), but when you integrate you should start from the time the mass moves.

SO change in momentum equal change in impulse only from the time they're moving

you find speed and c) is trivial
P = F v, both at your final time

Answer 3

have you got the answer for b & c?

Answer 4

*The same goes for part b), *

don't you have to integrate over the resulting force, that is (beta*t^2-friction)?

Answer 5

I still can't understand how to integrate... would you show me?