Analyzing Energy Conservation in a Swinging System

[Giuseppe]

Hey, I was wondering if anyone can help analyze this problem with me. Here is the question.

A swing seat of mass M is connected to a fixed point P by a massless cord of length L. A child also of mass M sits on the seat and begins to sing with zero velocity at a position of which the cord makes a 60 degree angle with the vertical. The swing continues down until the cord is exactly vertical at which the time the child jumps off in a horizontal direction. The swing continues in the same direction until the cord makes a 45 degree angle with the vertical. At that point, it begins to swing in the reverse direction. With what velocity relative to the ground did the child leave the swing?

I known I have to use conservation of energy. Is this basically asking to find the speed of the swing at the low point. If so, why would you need to know that the swing goes up to 45 degrees. I am not sure how to link the two pieces of information concerning the angles in order to solve the problem

 

[arildno]

No, it's bit trickier than that.
Hint:
When the child leaves the seat, the angular momentum of system child+seat with respect to P must be conserved..(why?)

Of course, you'll need to use energy conservation as well..

 

[Giuseppe]

would that be because there is no external torques acting on the system?

 

[arildno]

would that be because there is no external torques acting on the system?

Exactly!
At that moment, the torque from gravity is zero.
Assume that the child gains a leaving velocity relative to the seat, but that the cord remains strictly vertically aligned in the time period from the child has equal velocity with the seat to the time when it has reached its leaving velocity.

Use energy conservation to determine what the velocity of the seat must be just prior and just after the child has left (that's where the angle info is needed).


Use this and conservation of angular momentum to determine the child's velocity.

 

[Giuseppe]

ok thanks, I got it!