# Simple/stupid question

1. Jul 4, 2009

### Puchinita5

1. The problem statement, all variables and given/known data

Figure 8-29 shows a thin rod, of length L and negligible mass,that can pivot about one end to rotate in a vertical circle. A heavyball of mass m is attached to the other end. The rod is pulled asidethrough an angle 6 and released.As the ball descends to its lowestpoint, (a) how much work doesthe gravitational force do on itand (b) what is the change in thegravitational potential energy ofthe ball-Earth system? (c) If thegravitational potential energy istaken to be zero at the lowestpoint, what is its value just as theball is released? (d) Do the mag-nitudes of the answers to (a)through (c) increase, decrease, orremain the same if angle 6 is in-creased?

2. Relevant equations
http://www.niu.edu/~debrown/Spring2009/Q4_5.09.pdf [Broken] if you click this link, scroll down to problem two for the image.

3. The attempt at a solution

i know how to do the problem, the only thing i cannot figure out is how to find the height. I googled the problem and someone said that the change in y should be L-Lcos(theta)....and when i used that it worked, but i don't know why. It's problably some simple geometry thing but I need to know what L-Lcos(theta) means in case i get a problem similar to this on an exam.

Last edited by a moderator: May 4, 2017
2. Jul 4, 2009

### rl.bhat

Draw an right angled triangle containing point of suspension, mass and the vertical line. If l is the length of the rod, its projection on the vertical line is L*cosθ. The remaining length on the vertical position of the rod is L - L*cosθ. That is the height through the mass m rises.