What Is the Ball's Velocity Before and After Collision?

[bman123]

Homework Statement

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.5 kg and 2.35 kg, and the length of the wire is 1.36 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

Homework Equations

not exactly sure

The Attempt at a Solution

I tried splitting into vector components but I'm not sure if this is right or what to do from there?

 

[Delphi51]

For (a), you have a ball changing its potential energy into kinetic energy.
I would start with
PE at the top = KE at the bottom
and then put in the detailed formulas for PE and KE.

 

[PotentialE]

well, considering the ball is moving around one point (where the wire connects to the ceiling), you can say it is moving 90degrees. this means, it it moving .25revolutions. this turns into an angular motion problem, or at least that's how I did it. You can find the time using the two vector components, so you're on the right track. Once you have the time, you also have the initial velocity of 0rev/sec, and a distance of .25rev. do the angular acceleration formula (well, the angular distance formula solved for acceleration) then you have the angular acceleration. With that, do the final velocity formula. Now, you know that in angular motion, the velocity vector is tangent to any point on the circle. So at this point in the circle, the ball is moving at the velocity you just found, meaning that it is moving ____rev/sec. convert this to meters/sec by finding the circumference of the circle, multiply to get the value in meters/sec. now you have the velocity of the ball just before the collision, I hope that helped to get you on the right track, good luck!