Work & GPE Homework Solution: m, R, h

[shell4987]

Homework Statement

In Fig. 8-33, a small block of mass m = 0.040 kg can slide along the frictionless loop-the-loop, with loop radius R = 14 cm. The block is released from rest at point P, at height h = 9R 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?
**image attached**

Homework Equations

w=mgh

The Attempt at a Solution

I've completed parts (a) through (c) and got those correct, however I cannot get a correct answer for (d) and (e), I used W=mgR and plugged in 0.040(9.8)(0.14)= 0.05488 mJ for (d) and then I used W=mg2R for (e) with plugging in 0.040(9.8)(2)(0.14)= 0.10976mJ... I need to convert these into joules and I did so and still got the wrong answer, I just want to know if I'm doing something wrong with the physics part of the problems?

 

[Doc Al]

The only thing wrong is your thinking that the units are mJ and need to be converted to Joules. U = mgy will give you the potential energy in Joules when you use standard units of kg and m, as is the case here.

 

[ogb p]

I would like to point out that the equations you are using for parts (d) and (e) are incorrect. The work done by gravity is given by W = mgh, where h is the change in height. In part (d), the height change is R, not 2R. So the correct equation would be W = mgh = (0.040 kg)(9.8 m/s^2)(0.14 m) = 0.05488 J. Similarly, in part (e), the height change is 2R, not 3R. So the correct equation would be W = mgh = (0.040 kg)(9.8 m/s^2)(2R) = 0.21952 J.

Additionally, for part (d), the gravitational potential energy at point Q should be taken as zero, not the bottom of the loop. This is because at point Q, the block is at the same height as the bottom of the loop, so there is no change in potential energy. Therefore, the potential energy at point Q would be the same as at the bottom of the loop, which is 0 J.

For part (e), the potential energy at the top of the loop can be found by using the equation PE = mgh, where h is the height of the block at the top of the loop. Since the block is at the same height as the top of the loop, the potential energy at the top of the loop would be the same as at point P, which is 0.35296 J.

I hope this helps clarify any confusion and provides a correct solution to the problem. Remember to always carefully consider the variables and equations you are using in physics problems.