(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a ball rolling on a frictionless horizontal surface of mass m and with velocity 5m/s. It collides elastically with a block mass 3m that is initially hanging at rest from a 50 cm wire that is hanging from the ceiling.Find the maximum angle through which the block swings after it is hit

2. Relevant equations

v=initial velocity=5

Rolling ball=m1=m

Hanging block = m2=3m

Velocity of hanging block after collision: (2m1/(m1+m2))v

Velocity of rolling ball after collision: ((m1-m2)/(m1+m2))v

3. The attempt at a solution

So using the two equations above I get that the velocity of the block is 2.5m/s and velocity of the ball is -2.5m/s. So far this agrees with the fact that this is an elastic collision the knietic energy afterwards is equal to the knietic energy before the collision.

So to find the angle I'm thinking that I need to find how far the block travels in the x direction, that way I can take the arctangent of the length of the string divided by the distance x to find an angle W.

I use the work energy theorem:W=Fx=max=K after. The masses will cancel so I have ax=K after. But the acceleration is just dv/dt which is a change in velocity over a very short time interval. My thinking is the collision is short enough to be called dt and since it goes from rest to 2.5 m/s that a=2.5.

X would then be (.5)(3)(2.5^2)/(2.5)=3.75 meters

angle W would then be arctan(375/50)=82 degrees

This does not seem reasonable since it would mean that the ball would leave the ground and some energy would be converted in to gravitation potential energy...help is appreciated

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# Homework Help: Elastic collision

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