Physics - Problem

Question

  A block of mass m compresses a spring (spring constant k) by a distance of d and starts from rest. It is launched from the spring and over the rough patch (length L and coefficient of kinetic friction μ_k) and then over the frictionless hill, which has a radius of curvature R at the top, as shown.

Find the normal force at on the mass at point B.Put your answer in terms of m,k,g,L,r, μ_k.

Answer 1

Hey Padmapriya,

I think I'm interpreting this problem correctly without the picture. But either way, some of these steps should help:

1. Start by finding the elastic potential energy stored in the spring. Add that to GPE (if there is any) to find the initial total energy in the system.
2. Calculate the work done by friction over the rough patch and subtract that from the initial total energy.
3. Now go to point B (the final position) and subtract whatever GPE the block has there from your total.
4. You should now have an expression for the KE of the block at point B. Now you can find the speed of the block at that point.
5. Now, to follow a curve of a circle at a specific speed, an object needs a net force equal to the centripetal force. Plug your v into the centripetal force formula to find what this net force needs to be.
6. Finally, consider a free-body diagram of the object at the top of this hill:
7. There is a downward force of gravity and an upward normal force - that's it.
8. Those 2 forces need to add up to equal your net force (aka centripetal force).

Hope this helps - good luck!