# Elastic Collision

1. Jan 2, 2012

### fobbz

1. The problem statement, all variables and given/known data

A ball of mass 5.0kg moving at a speed of 5.0m/s has a head on collision with a stationary bal of mass 6.0kg. If the collision were perfectly elastic what would be the speeds of the two balls after the collision?

2. Relevant equations

P = mv
KE = 0.5mv2
3. The attempt at a solution

Using together kinetic energy and momentum equations, I can solve for final velocities.

http://img855.imageshack.us/img855/6519/centralkootenayj2012010.jpg [Broken]

Is this correct?

Last edited by a moderator: May 5, 2017
2. Jan 2, 2012

### Flashlinegame

The formulas for elastic collisions are:
v1 = u1(m1-m2)/(m1+m2)
v2 = 2m1u1/(m1+m2)

v1 = 5(5-6)/(6+5) = -5/11 m/s = -.45 m/s
v2 = (2*5*5)/(5+6) = 50/11 m/s = 4.5 m/s

So you got the right answers if you add a negative sign to v1 since it bounces backwards after the collision.

Last edited by a moderator: Jan 3, 2012
3. Jan 2, 2012

### fobbz

How do you know that the first ball will bounce backwards?

Last edited by a moderator: Jan 3, 2012
4. Jan 2, 2012

### cupid.callin

My advice would be not to rely on these formulas and use conservation of KE and momentum conservation and the equation of restitution ... with these 3 things you can solve nearly all collision problems.

PS:
KE Coservation: $\frac{1}{2}{m_1u_1}^2 + \frac{1}{2}{m_2u_2}^2 = \frac{1}{2}{m_1v_1}^2 + \frac{1}{2}{m_2v_2}^2$ - valid only when e=1

Momentum Conservation: $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$ - valid for all $e\in[0,1]$

Eqn of coefficient of restitution: $(v_2 - v_1) = e(u_1 - u_2)$

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