What Are the Velocities and Forces in This Elastic Collision?

In summary, using the conservation of momentum and energy, we can determine that after the collision, the first object will have a velocity of -1.75m/s and the second object will have a velocity of 3.15m/s. To find the force exerted on each other, we would need to use the impulse-momentum theorem and calculate the change in momentum over the duration of the collision.
  • #1
chrisfnet
39
0

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!
 
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  • #2
To find the velocities of the objects after collision, you have to use the conservation of momentum and energy.
 
  • #3
rl.bhat said:
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?
 
  • #4
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
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.
 

FAQ: What Are the Velocities and Forces in This Elastic Collision?

What is an elastic collision?

An elastic collision is a type of collision between two objects where both kinetic energy and momentum are conserved. This means that the total energy and total momentum of the system before and after the collision are equal.

How is velocity affected in an elastic collision?

In an elastic collision, the velocities of the objects involved are affected by the collision but they are not changed in magnitude. The velocities may change direction, but the total kinetic energy of the system remains the same.

What is the difference between elastic and inelastic collisions?

The main difference between elastic and inelastic collisions is that in an inelastic collision, kinetic energy is not conserved. This means that the total energy of the system after the collision is less than the total energy before the collision. In an elastic collision, both kinetic energy and momentum are conserved.

Is the coefficient of restitution the same as elasticity?

No, the coefficient of restitution and elasticity are not the same. The coefficient of restitution is a measure of how bouncy a collision is, while elasticity is a measure of how well an object can return to its original shape after a collision. However, the two are related since a higher coefficient of restitution indicates a more elastic collision.

How do you calculate the final velocities in an elastic collision?

The final velocities in an elastic collision can be calculated using the conservation of momentum and conservation of kinetic energy equations. By setting the total initial momentum and total initial kinetic energy equal to the total final momentum and total final kinetic energy respectively, you can solve for the final velocities of the objects involved in the collision.

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