A physics question that uses momentum and collision concepts

Question

A 3kg steel ball attached to a string is given an initial velocity of 1.8m/s and swings through an angle of 60 degrees, colliding with a 4kg steel cube also suspended by a string, initially at rest

 

if the two collide elastically what will be the maximum height reached by the sphere and the cube after the collision

 

if the two collide inellastically with a coefficient restitution of .60, what will be the velocity immediatly after the collision?

 

if the two collide totally inelasticaly what will be the velocity immediatly after the collision?

 

Answer 1

First, find the speed of the ball just before the ball collides with the cube using energy conservation.  From this initial velocity, use momentum conservation (Equation 1) for the following 3 cases.

 

There are three given scenarios for the coefficient of restitution:

 

e = 1 for elastic collision,

 

e = 0.60 for the inelastic collision, and 

 

e = 0 for the totally inelastic collision.

 

 

The coefficient of restitution is the ratio of the relative velocity of the objects after the collision to their relative velocity before the collision.  e = (v_2f - v_1f)/(v₁₀ - v₂₀)  (Equation 2)

 

Write Equations 1 and 2 for each collision type to find the final velocities.  Use the final velocities for the elastic collision and energy conservation for each object to find their maximum heights after the collision.  Good luck.