# How Does Elastic Collision Affect Particle Momentum?

• Learning Curve
She knows the equation for momentum and that the collision is elastic, meaning no energy is lost. She sets up an equation using the initial and final momentums and solves for P2, but is unsure where to go from there. You can use the relationship between relative velocities to find the mass of the unknown particle.In summary, Dorothy is struggling with a question about an elastic collision between a proton and a stationary particle. She knows the equation for momentum and that the collision is elastic, but is unsure how to find the mass of the unknown particle. You can use the relationship between relative velocities to solve for the mass.
Learning Curve
Here's a question from my workbook that I can't seem to figure out.

A proton (mass = 1.6 x 10^27 kg) moves with a speed of 6 Mm/s. Upon colliding elastically with a stationary particle of unknown mass, the proton rebounds on its own path with a speed of 3.6 Mm/s. Find the mass of the unknown particle.

Let's start with what I know. I know that momentum = mass times velocity.
or p = mv

I also know that since it's elastic, it isn't losing any energy.

So I used the equation P1 + P2 = P1 + P2

(1.67 x 10^-27 kg)(6 Mm/s) + 0 = (1.67 x 10^-27 kg)(-3.6 Mm/s) + P2

I said 3.6 Mm/s was negative since it was in the opposite direction.

So from there I got:

3.006 x 10^-20 kg(Mm/s) = 1.08216 x 10^-26 kg(Mm/s) + P2

P2 = 1.923 x 10^-26

But, from there I'm not sure where to go. I'm trying to find the mass of this particle, but I need to know it's velocity. Any help or hints is appreciated.

The relative velocities of the bodies before and after an elastic collision have a predictable relationship. You could use that to find the mass.

Dorothy

I can provide some assistance with this problem. First, you have correctly identified the equation for momentum, p = mv. In this case, we are dealing with an elastic collision, which means that the total momentum before the collision is equal to the total momentum after the collision. This is known as the conservation of momentum principle.

Using this principle, we can set up an equation with the initial momentum of the proton (p1) equal to the final momentum of the proton (p1') plus the final momentum of the unknown particle (p2). This can be written as:

p1 = p1' + p2

Since we know the mass and velocity of the proton before and after the collision, we can plug those values into the equation:

(1.6 x 10^-27 kg)(6 Mm/s) = (1.6 x 10^-27 kg)(3.6 Mm/s) + p2

Solving for p2, we get:

p2 = 2.88 x 10^-27 kg(Mm/s)

This is the final momentum of the unknown particle after the collision. Now, we can use the same equation for momentum, p = mv, to solve for the mass of the unknown particle. We know the momentum (p2) and the velocity (3.6 Mm/s), so we can rearrange the equation to solve for mass:

m = p/v

Plugging in the values, we get:

m = (2.88 x 10^-27 kg(Mm/s)) / (3.6 Mm/s) = 8 x 10^-28 kg

Therefore, the mass of the unknown particle is 8 x 10^-28 kg. I hope this helps you solve the problem in your workbook. Remember to always use the principles of conservation of momentum and energy in elastic collisions.

## What is momentum?

Momentum is a measure of an object's motion, taking into account both its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

## How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = m * v, where p is momentum, m is mass, and v is velocity.

## What is the unit of measurement for momentum?

The unit of measurement for momentum is kilogram-meters per second (kg*m/s) in the SI system. In the imperial system, the unit is pound-feet per second (lb*ft/s).

## What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before an event is equal to the total momentum after the event. This means that momentum is conserved and cannot be created or destroyed, only transferred between objects.

## How does momentum relate to Newton's laws of motion?

Momentum is closely related to Newton's laws of motion. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. The second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. This can be rewritten as F = m * a = m * (Δv/Δt) = m * (v2 - v1)/Δt, which shows that force is directly proportional to a change in momentum over time. The third law states that for every action, there is an equal and opposite reaction. This means that when two objects interact, their momenta will change in opposite directions but with equal magnitudes.

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