Homework Help: 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: $(v_2 - v_1) = e(u_1 - u_2)$