Elastic Collision kinetic energy and momentum

[fobbz]

Homework Statement

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?

Homework Equations

P = mv
KE = 0.5mv²

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

Is this correct?

 

[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.

 

[fobbz]

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.

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

 

[cupid.callin]

Homework Statement

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?

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

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

 

[asteriatic]

Your attempt at a solution is correct. The final velocities can be calculated using the equations P = mv and KE = 0.5mv^2, as shown in the image. In an elastic collision, both momentum and kinetic energy are conserved, so the total momentum and total kinetic energy before and after the collision should remain the same. By setting up and solving the equations for momentum and kinetic energy, you can find the final velocities of the two balls after the collision. Good job! It is important to use both equations to fully analyze the motion and energy of objects in a collision.