Elastic Collision of Two Particles: Solving for Final Velocity

Therefore, we can set the final momentum of the system equal to the initial momentum: pf = pi. In this case, the initial momentum is just the momentum of the first particle, since the second particle was initially at rest. So, we can say pf1 + pf2 = pi1 + pi2, or mvf1 + (3m)vf2 = mvi1. Since we already have an expression for vf1 in terms of vf2 from our original attempt at a solution, we can substitute that in: mv1/3 + (3m)vf2 = mvi1. Solving for vf2, we get vf2 = (v1 - vi1)/4. This is where the answer of v
  • #1
v3r
5
0

Homework Statement


Particle 1 of mass m moving with speed v in the +x direction has an elastic
collision with particle 2 of mass 3m which was originally at rest. After the collision,
particle 2 is moving in the +x direction. What is its speed?

Homework Equations


deltap = 0
pf1 + pf2 = pi1 + pi2

The Attempt at a Solution


Wouldn't it just be
pf2 = pi1
3mvf2 = mv1
vf2 = v1/3

How come the answer is v1/2 instead? Help please..
 
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  • #2
v3r said:

The Attempt at a Solution


Wouldn't it just be
pf2 = pi1
You can't assume that the first particle stops and all its momentum goes to the second particle.

Hint: What does elastic mean?
 
  • #3
Elastic means no change in internal energy
DeltaE = 0
DeltaK + DeltaEint = 0
DeltaK = 0
Kf1 - Ki1 + Kf2 = 0

0.5mvf1^2 - 0.5mvi1^2 + 0.5(3m)vf2^2 = 0
0.5(3m)vf2^2 = 0.5mvi1^2 - 0.5mvf1^2

There's two unknowns, vf2 and vf1
Is this setup wrong?
 
  • #4
v3r said:
0.5mvf1^2 - 0.5mvi1^2 + 0.5(3m)vf2^2 = 0
0.5(3m)vf2^2 = 0.5mvi1^2 - 0.5mvf1^2

There's two unknowns, vf2 and vf1
Is this setup wrong?
No, it's fine. You just need another equation--conservation of momentum. Then you'll have two equations and two unknowns.

In any collision, momentum is conserved; in an elastic collision, kinetic energy is also conserved.
 

1. What is a simple elastic collision?

A simple elastic collision is a type of collision between two objects in which the total kinetic energy of the system remains constant. This means that the total energy before the collision is equal to the total energy after the collision.

2. How is the momentum conserved in a simple elastic collision?

In a simple elastic collision, the total momentum before the collision is equal to the total momentum after the collision. This is because there is no external force acting on the system, so the total momentum remains constant.

3. What are the key assumptions made in a simple elastic collision?

The key assumptions made in a simple elastic collision include: 1) the objects involved are perfectly elastic, meaning they do not deform or lose any energy during the collision, 2) the collision occurs in a frictionless environment, and 3) the objects involved are point masses with no rotational or angular motion.

4. How is the coefficient of restitution related to a simple elastic collision?

The coefficient of restitution, denoted by e, is a measure of the elasticity of a collision. In a simple elastic collision, the coefficient of restitution is equal to 1, indicating a perfectly elastic collision. This means that the objects involved bounce off each other without any loss of energy.

5. Can a simple elastic collision occur between more than two objects?

Yes, a simple elastic collision can occur between multiple objects as long as the key assumptions are met. In this case, the total kinetic energy and momentum of the system will still be conserved, but the calculations may be more complex as they involve multiple objects.

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