# PE and KE problem

1. Oct 23, 2012

### vysero

In Fig. 8-31, a small block of mass m = 0.032 kg can slide along the frictionless loop-the-loop, with loop radius R = 12cm. The block is released from rest at point P, at height h = 5.0R above the bottom of the loop. How much work does the gravitational force do on the block as the block travels from point P to (a) point Q and (b) the top of the loop? If the gravitational potential energy of the block-Earth system is taken to be zero at the bottom of the loop, what is that potential energy when the block is (c) at point P, (d) at point Q, and (e) at the top of the loop? (f) If, instead of merely being released, the block is given some initial speed downward along the track, do the answers to (a) through (e) increase, decrease, or remain the same?

I believe that the relevant equations are:
w=fd and w=mgh and maybe ke=1/2mv^2

Well I believe if I could figure out what the the specific heights at the given points are then I could make some calculations for instance: (a) If I new what the height at point Q was I would say the work would be mgh but I am having trouble understanding what they want me to do with the given height being 5.0R! Also, I believe the answer to (f) is remain the same right because work and PE don't have anything to do with velocity.

Last edited: Oct 23, 2012
2. Oct 23, 2012

### haruspex

The heights of points P and Q are clearly given in the diagram: h and R respectively, and you know h = 5R.
Q appears to be intended as the height of the centre of curvature of the final loop. The radius is given as R, so what would the height of the top of the loop be?

3. Oct 23, 2012

### vysero

Well let's start with the height at Q. The height at is 5R or 5*12cm which is 60cm. So then point Q is 60cm - 12cm which is 48cm right? That's .48m and if w = mgh then it should be (.032)(9.8)(.48) = .150528 J which doesn't seem right to me.

4. Oct 23, 2012

### haruspex

No, P is 5R above the bottom of the loop, and Q is R above the bottom of the loop. Q is 48cm below P, but I think they want the PE relative to 0 at the bottom of the loop.