# Momentum question asking ratio of final 2 velocities

• hamza2095
In summary, the problem involves a cart with a mass of M moving at 3V colliding with a stationary mass of M. The ratio of the two final velocities can be determined by using the equations for momentum and kinetic energy. After solving the equations, it is found that the ratio of the final velocities is 3:0 or 0:3, which makes sense for an elastic collision.
hamza2095

## Homework Statement

A cart mass of M moving at 3V (right) collides with a stationary mass of M, Determine the ratio of the two final velocities if the collision is elastic

p=mv
ek=(mv^2/2)

## The Attempt at a Solution

m1v1=m1v1'+m2v2'

Since the masses are all equal and v1 is 3V the equation becomes
3 = v1' + v2'

Since the collision is elastic the total energy afterwards equals the total energy afterwards

Ek=(mv^2/2)

so Ek1=Ek1'Ek2'
and since every term is over 2,and the masses equal the equation simplifies to
v1^2=v1'^2+v2^2

After rearranging the first equation you get v1' = v2'-3, and then plug that into the energy equation to get
9= 2v2'^2 -6v2-9
0=2v2'^2 -6v2

after applying the quadratic equation you get 3 or 0, and since the velocity has to change v2' is 3, subsequently v1' is 0 so the ratio is 3:0, or 0:3

3:0 doesn't make sense to me for some reason but I can't find any mistake in what I did, is this right?

I can't find a mistake either.
Check it by sliding a coin against a similar coin on a flat table (aim for a central collision)

By the way: if an initial speed of 3V is given, your calculations should be in units of V, e.g.
3 MV = MV1'+ MV2'

hamza2095 said:
3:0 doesn't make sense to me
It's quite correct. Look for a video of Newton's cradle.
With equal masses and elastic collision, swapping over the two initial speeds to get the final speeds must be right. It would have the same momentum and the same energy.

## What is momentum?

Momentum is a measure of an object's motion, determined by 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 is: momentum = mass x velocity.

## What is the equation for the conservation of momentum?

The equation for the conservation of momentum states that the total momentum of a closed system remains constant over time. This can be written as: initial momentum = final momentum.

## What is the relationship between velocity and momentum?

Velocity and momentum are directly proportional. This means that as velocity increases, so does momentum. This is because the greater the velocity, the greater the object's mass in motion and thus the greater its momentum.

## How does an object's mass affect its momentum?

An object's mass directly affects its momentum. This means that the greater the mass of an object, the greater its momentum, given the same velocity. This is because a heavier object requires more force to change its velocity, resulting in a greater momentum.

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