A) Assume the mass of a pendulum is 3kg. Calculate the work done by the pendulum on the mass from 0 degrees to 180 degrees ( you will need to integrate with respects to d(theta ) instead of dx
given: the mass at the end of the string experiences a restoring force given by: F=-mgsin(theta) i
B) compare the work done in part A to the amount of potential energy given to the mass as it moves from 0 degrees to 180 degrees using mgh
I did not do this right but here is some of my work
A) -mgsin(0)
-(3kg)(9.8)sin(0)
Integral sinx dx=-cosx + C
W=29.4cos(180)-29.4cos(0
-29.4-29.4=-58.8
W=-58.8 J
B) I did this completely wrong
29.4sin(180) =0
H=L(1-cos0)
PE=mgl(1-Cos0)
Integrate: PE=3*9.8l(1-cos(180)
PE=mg(d/2)sin(180)
29.4sin(180)= 0 potential energy