Why Is the Correct Answer mgh/4 in This Energy Problem?

[nish123]

Homework Statement

Hello All !

I have this question which I can't seem to get the correct ans to.. maybe I am missing something.. (Please refer to attachment)

Homework Equations

POtential energy = mass x g x h

The Attempt at a Solution

ok initial amt of energy = m x g x h

final energy state =( mgh/4 + mgh/4 )= mgh/ 2

so mgh - mgh/2 = mgh/2 (my ans)

apparently correct ans is mgh/4

help , pls ? thanks !

 

[gneill]

Hi nish123, Welcome to Physics Forums.

When dealing with changes in potential energy, you want to consider the change in elevation of the center of mass.

 

[nish123]

ahh, got it!... thanks a ton
gneill and
ResscuedByMary

point i was missing was "When dealing with changes in potential energy, you want to consider the change in elevation of the center of mass."Thanks again !

 

[nish123]

thanks ResscuedByMary i now understand your explanation too...

"When dealing with changes in potential energy, you want to consider the change in elevation of the center of mass." was told by
gneill as above... thanks both !

 

[Nickie]

Hello! I understand your confusion with this question. It is important to remember that energy is always conserved, meaning that the initial energy state must equal the final energy state. In this case, the initial energy state is mgh, but the final energy state is not (mgh/4 + mgh/4). Instead, the final energy state is mgh/4, since the object is only moving up half the distance it initially did. This is because the object is moving in a circular motion, so the distance it travels up is half the distance it travels around the circle. Therefore, the correct answer is mgh/4, and your initial attempt at the solution is incorrect. I hope this helps clarify the question for you.