What Are the Velocities and Forces in This Elastic Collision?

[chrisfnet]

Homework Statement

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?

Homework Equations

-v₂i + v₁i = -v₁f + v₂f

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!

 

[rl.bhat]

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

 

[chrisfnet]

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

How would I integrate the conservation of energy?

 

[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?

 

[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"

If so, your answer will come out different.