Potential Energy problem homework

[aspirare21]

Hello guys I need your help T__T I'm new here.. ^__^

Homework Statement

A girl weighing 470N hangs suspended on the end of a rope 8 meters long. What will be her gain in potential energy when a boy swings her to one side so that the rope makes an angle of 35º with the vertical? gravity= 9.7 m/sec²

I need the answer to be exactly 679.5 Joules.. My professor wants that I use an equation with Fg? (Free body diagram)? Or any solution that will leads to the exact answer..

Homework Equations

PE=mgh

The Attempt at a Solution

PE''=mgh mg (470N) x h (8 meters)
=3760

PE'=mgh 470 x (cos 35º) x 8
=3080

3760-3080=680

 

[tiny-tim]

Welcome to PF!

Hello aspirare21! Welcome to PF!

A girl weighing 470N hangs suspended on the end of a rope 8 meters long. What will be her gain in potential energy when a boy swings her to one side so that the rope makes an angle of 35º with the vertical? gravity= 9.7 m/sec²

I need the answer to be exactly 679.5 Joules.. My professor wants that I use an equation with Fg? (Free body diagram)? Or any solution that will leads to the exact answer..
…
PE''=mgh mg (470N) x h (8 meters)
=3760

PE'=mgh 470 x (cos 35º) x 8
=3080

3760-3080=680

Well, I get exactly the same answer as you (not 679.5).

(btw, using 1- cos35º in the first place would have been quicker and neater )

Also, I don't understand what your professor thinks g has to do with it (nor why it's only 9.7 ! ) … the weight is given in Newtons.

(I assume the equation your professor is thinking of is PE = (minus) work done = force "dot" distance = F_g.x = F_gh )

 

[aspirare21]

Hello tiny-tim :)

I myself is confuse on how he derive the g=9.7 m/sec². He wants us to show a free body diagram on how to solve it.. Maybe putting tension,normal force,etc. I don't know if the formula or the pendulum is applicable here.. But this problem doesn't have a velocity. :(