# Solve Momentum Problem: White & Red Pool Balls Collide

• aeroengphys
Then you can solve for the remaining variable. In summary, to solve for the velocities of the white and red pool balls after a perfectly elastic collision, you can use the conservation of momentum and kinetic energy equations to create a system of equations and solve for the velocities. The conservation of momentum equation is p1 + p2 = p1' + p2' and the conservation of kinetic energy equation is 1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2. By substituting one equation into the other, you can solve for v1' and v2'.
aeroengphys

## Homework Statement

"A white pool ball (m1 = .3kg) moving at a speed of Vo1 = 3m/s collisdes head-on with a red pool ball (m2 = .4kg) initially moving at a speed of Vo2 = -2m/s. Neglecting friction and assuming the collision is perfectly elastic, what is the velocity of each ball after the collision?"

Underneath the question are two diagrams, a diagram labeled before (shows a white and red ball moving towards one another) and a diagram labeled after (shows the collision and the balls moving in opposite directions).

## Homework Equations

p before = p after

## The Attempt at a Solution

p before = p after
p1 + p2 = p1' + p2'
m1v1 + m2v2 = m1v1' + m2v2'
(.3kg)(3m/s) + (.4kg)(-2m/s) = (.3kg)v1' + (.4kg)v2'
.1 Ns = .3v1' + .4v2'

This is where I'm getting stuck...Since the balls have different masses, the velocities v1' and v2' will be different, but how can you make the two variables into one, and solve for the speeds?

Any help will be appreciated.

Perfectly elastic collisions also conserve kinetic energy.

i'm still kind of confused...how exactly do you relate kinetic energy and momentum. I know that KE = 1/2mv^2...so does that mean you can solve v1' and v2' independly using just KE?

aeroengphys said:
i'm still kind of confused...how exactly do you relate kinetic energy and momentum. I know that KE = 1/2mv^2...so does that mean you can solve v1' and v2' independly using just KE?

No, the conservation of kinetic energy equation will provide you with a second equation for v1' and v2'. Consider it in the same way in which you have considered the conservation of momentum, i.e total KE before = total KE after. This and the conservation of momentum equation will enable you to solve for v1' and v2'.

You can use one equation to eliminate one variable by substituting into the other equation.

## What is momentum and why is it important in solving pool ball collisions?

Momentum is a physical quantity that describes the motion of an object. In the context of pool ball collisions, it refers to the amount of motion that a ball has. It is important in solving these collisions because it allows us to predict the outcomes of the collisions and to understand the conservation of energy and momentum.

## How do you calculate the momentum of a pool ball?

The momentum of a pool ball can be calculated by multiplying its mass by its velocity. The formula for momentum is: p = m * v, where p is momentum, m is mass, and v is velocity. The units for momentum are kg*m/s.

## What is the law of conservation of momentum and how does it apply to pool ball collisions?

The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. In other words, the total momentum of the system is conserved. This law applies to pool ball collisions because the pool balls are considered a closed system, meaning that no external forces are acting on them during the collision.

## What information do you need to solve a momentum problem involving pool ball collisions?

In order to solve a momentum problem involving pool ball collisions, you will need to know the mass and velocity of each ball before and after the collision. You will also need to know the direction of motion of each ball. Additionally, you will need to know if there are any external forces acting on the system, such as friction or air resistance.

## Can momentum be transferred between pool balls during a collision?

Yes, momentum can be transferred between pool balls during a collision. This is known as an elastic collision, where the total momentum of the system is conserved and the kinetic energy is also conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, and the total momentum is still conserved.

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