# Pendulum find length when it rotates

## Homework Statement

A pendulum made of a string and a sphere is able to swing in a vertical plane. The pendulum is released from a position of 70 degree from vertical. The string hits a peg located a distance d below the point of suspension and rotates about the peg. Find the smallest value of d (highest peg position) in order for the sphere to swing in a full circle centered on the peg.

How do i start this???
I understand this is hard with out a pic sorry guys.

diazona
Homework Helper
I would suggest using conservation of energy. If the peg is located at the smallest value of d, the sphere should have just barely enough energy to make it up to the top of its full circle.

yeah I thought about that but I could use it at the beginning and the point where the ball barely thouch the floor.
so the equation I use it
mgh=.5mv^2
but that is not going to give me the d. The thing is that the length of the string is 10 m to begin with but I want to find out what is the new length of the string when it rotates around the peg. if you see where I am getting at.

diazona
Homework Helper
Can the length of the string change? Because I don't think you mentioned that in the problem...

well the length of the string is changing
so the string is really 10 m right and then there this stick or peg some where at distance d
which causes the rope to rotate. what is the distace d or the rope distance after it rotated both d are the same

diazona
Homework Helper
Sure, the string rotates (or rather, part of it rotates), but that doesn't mean the length of the string changes. I'm fairly confident that the length of the string is supposed to be constant; it seems that you may have been misinterpreting the problem.