Vertical Circle Rod: Work and Energy Calculations | Simple Homework Question

[Puchinita5]

Homework Statement

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?

Homework Equations

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

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.

 

[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.