# Elastic Collision and velocity

1. Oct 27, 2009

### chrisfnet

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

A 0.24kg object traveling rightward at 3.5m/s collides head-on and elastically with a 0.40kg object traveling leftward at 2.1m/s.

What are their velocities after the collision?

If the objects are in contact for 0.010s during the collision, what is the magnitude of the average force that they exert on each other?

2. Relevant equations

-v2i + v1i = -v1f + v2f

3. The attempt at a solution

Initial Momentum = 0.24kg(3.50m/s) + 0.40kg(2.1m/s)
Initial Momentum = 1.68 kg*m/s

1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f

* Now I find a substitution. *

-v2i + v1i = -v1f + v2f

-v2i + v1i = -2.1m/s + 3.5m/s = 1.40m/s
1.40m/s = -v1f + v2f
v2f = v1f + 1.40m/s

* Now I substitute it back into the above equation. *

1.68kg*m/s = 0.24kg*v1f + 0.40kg*(v1f + 1.40m/s)
1.68kg*m/s = 0.24kg*v1f + 0.40kg*v1f + 0.56kg*m/s
1.12kg*m/s = 0.64kg*v1f
-1.75m/s = v1f (Negative to indicate direction.)

* Now I substitute v1f into the original equation. *

1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f
1.68kg*m/s = 0.24kg * 1.75m/s + 0.40kg*v2f
v2f = 3.15m/s

I have no idea how to figure out the force exerted on each other. Could someone help here, and also verify that the above answers are correct? Thanks!

2. Oct 27, 2009

### rl.bhat

To find the velocities of the objects after collision, you have to use the conservation of momentum and energy.

3. Oct 27, 2009

### chrisfnet

How would I integrate the conservation of energy?

4. Jan 3, 2010

### zdotcom

I am trying to solve a similar problem and I have a question.

How did you get this one: "-v2i + v1i = -v1f + v2f" ?

how is this derived? How did ou determine "-v1f + v2f" where v1f is negative if mass is not part of the equation?

5. Jan 3, 2010

### zdotcom

I am trying to solve a similar problem and I have a question.

How did you get this one: "-v2i + v1i = -v1f + v2f" ?

how is this derived? How did ou determine "-v1f + v2f" where v1f is negative if mass is not part of the equation?

Besides, if v1f is negative, then shouldn't v1f in this equation be negative as well?
"1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f"