How to calculate a trapeze/ pendulum's arc distance

[katkinson]

Homework Statement

This is an update to an earlier post. Since then, I now understand that a pendulum stops when its tension force= mg sin(theta)--because then centripetal force will=0, so velocity will be 0. However, now I am trying to determine how a trapeze would work on the moon.

Homework Equations

KE=1/2 mv^2
PE= mgh
T=2π√(L/g)
Fc=mv^2/r
Ft=Fc-mg sin(theta)
KE (initial) + PE (initial) = KE (final) + PE (final)

The Attempt at a Solution

Drawing a free body diagram, I determined that when an object peaks during its swing the following is true: Because the object is stopped, Fc=0. Because Fc=0 and the radius and mass are supposedly constant, velocity must=0. (That also means that it is 100% PE). Because Ft - mg sin (theta) = 0, then Ft= mg sin (theta). I am trying to determine what sin (theta) is, because then I can determine the length of the swing on the moon. However, I do not know how to determine Ft so I thought I would try using the other method while using T=2π√(L/g). However, I do not know how I can use the time to determine the length of the arc

Thanks so much

 

[voko]

The amplitude (length of swing) depends on how fast the pendulum was pushed to begin with, i.e., its speed when it is at the lowest point. That, and conservation of energy, result in a particular amplitude.