# Solve m2 & v2' Elastic Collision: Ball A & B Velocity/Mass

• erikewell
In summary: It states that the total momentum of the objects after the collision is the same as it was before the collision. This means that the x and y components of momentum are conserved. This is huge because it allows us to solve for x and y without having to know the other equation's values.
erikewell
"Ball A with mass 4kg is moving with a velocity of 8m/s North when it crashes into Ball B with unknown mass moving with a velocity of 6 m/s West. This collision is perfectly elastic. If Ball A ends up moving with a velocity of 6.5 m/s @ 120 degrees after the collision, find the final mass and final speed of Ball B if it moves at an angle of 160 degrees after the collision."

The formula to calculate an elastic collision is m1v1 + m2v2 = m1v1' + m2v2', where v1' and v2' represent velocities after the collision, m1 and 2 meaning masses and v1 and 2 meaning velocity before collision.

I know what I have to do, but I have no idea how to rearrange the equation to solve for both m2 and v2'. Could you guys help me with solving this? I'd really appreciate it.

erikewell said:
"Ball A with mass 4kg is moving with a velocity of 8m/s North when it crashes into Ball B with unknown mass moving with a velocity of 6 m/s West. This collision is perfectly elastic. If Ball A ends up moving with a velocity of 6.5 m/s @ 120 degrees after the collision, find the final mass and final speed of Ball B if it moves at an angle of 160 degrees after the collision."

The formula to calculate an elastic collision is m1v1 + m2v2 = m1v1' + m2v2', where v1' and v2' represent velocities after the collision, m1 and 2 meaning masses and v1 and 2 meaning velocity before collision.

I know what I have to do, but I have no idea how to rearrange the equation to solve for both m2 and v2'. Could you guys help me with solving this? I'd really appreciate it.

What does it mean for a collision to be "perfectly elastic"? Perhaps this tells us something about one of the variables, so we can solve for the other unknown?

Also, what does conservation of momentum tell us?

To expand a little bit and perhaps shed some more light about what I'm getting at, remember that momentum is a vector quantity and can therefore be broken into x and y parts. Conservation of momentum tells us something very important relating to this that we can use to solve these types of problems.

## 1. What is an elastic collision?

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

## 2. How do you solve for m2 and v2 in an elastic collision?

In order to solve for m2 and v2 in an elastic collision, you will need to use the equations of conservation of momentum and conservation of kinetic energy. These equations can be set equal to each other and manipulated to solve for the unknown variables.

## 3. What is the relationship between mass and velocity in an elastic collision?

In an elastic collision, the mass and velocity of the objects are inversely proportional. This means that as the mass of an object increases, its velocity will decrease in order to conserve the total kinetic energy of the system.

## 4. How does the coefficient of restitution affect an elastic collision?

The coefficient of restitution is a measure of the elasticity of a collision. In an elastic collision, the coefficient of restitution will be equal to 1, meaning that the objects will bounce off each other with no loss of kinetic energy. A lower coefficient of restitution indicates a less elastic collision, where some kinetic energy is lost.

## 5. Can an elastic collision occur between objects of different masses?

Yes, an elastic collision can occur between objects of different masses. The conservation of momentum and kinetic energy equations will still hold true, and the final velocities of the objects will be determined by their masses and initial velocities.

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