Work by Gravity / Conservative Forces

[Jamieee]

A ball is moved from point A to point B, to point C, to point D, to point E, and back to point A. So, to make things easier... here's a diagram of the problem.

http://img181.imageshack.us/img181/125/conservativeforcesvy3.jpg

We were asked to prove (mathematically) the concept that gravity (in this diagram) is a conservative force, and why the angle in the diagram is disregarded.

The following equations were given (and I don't really understand them )...

W = W (A to B) + W (B to C) + W (C to D) + W (D to E) + W (E to A)
W = 0 + (-mgh) + 0 + (-mgh) + (mgh)
W = 0 <--- This has to be proven as well.

I'm also wondering why W (D to E) became (-mgh) instead of Fxcos(theta).

Help please... Thanks in advance!

--- Jamie

 

[Astronuc]

W = W (A to B) + W (B to C) + W (C to D) + W (D to E) + W (E to A)
W = 0 + (-mgh) + 0 + (-mgh) + (mgh)

It appears the sign convention is - for upward movement and - for downward movement, i.e. the if ball ascends then gravity does - work, and if the ball descends then gravity is doing + work. If the ball were in freefall (downward) the gravitational potential energy would be transformed into the balls kinetic energy which would increase.

Please be careful with the distance h. One has used h repeatedly, but there are different elevations or heights involved.

If h is the distance AE, then BC < h. The height between D and E is DE sin$\theta$, and then h= AE = BC + DE sin$\theta$.

 

[Jamieee]

Thank you. So much. I get it now. :D