# High School Physics : Understanding Conservation of Momentum

## Example Questions

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### Example Question #1 : Understanding Conservation Of Momentum

A man with a mass of is painting a house. He stands on a tall ladder of height . He leans over and falls straight down off the ladder. If he is in the air for  seconds, what will be his momentum right before he hits the ground?

Explanation:

The problem tells us he falls vertically off the ladder (straight down), so we don't need to worry about motion in the horizontal direction.

The equation for momentum is:

We can assume he falls from rest, which allows us to find the initial momentum.

.

From here, we can use the formula for impulse:

We know his initial momentum is zero, so we can remove this variable from the equation.

The problem tells us that his change in time is  seconds, so we can insert this in place of the time.

The only force acting upon man is the force due to gravity, which will always be given by the equation .

### Example Question #2 : Momentum

ball is thrown west at  and collides with a  ball while in the air. If the balls stick together in the crash and fall straight down to the ground, what was the velocity of the second ball?

Explanation:

We know that if the balls fell straight down after the crash, then the total momentum in the horizontal direction is zero. The only motion is due to gravity, rather than any remaining horizontal momentum. Based on conservation of momentum, the initial and final momentum values must be equal. If the final horizontal momentum is zero, then the initial horizontal momentum must also be zero.

In our situation, the final momentum is going to be zero.

Use the given values for the mass of each ball and initial velocity of the first ball to find the initial velocity of the second.

The negative sign tells us the second ball is traveling in the opposite direction as the first, meaning it must be moving east.

### Example Question #1 : Understanding Conservation Of Momentum

car travelling at  rear ends another  car at rest. The two bumpers lock and the cars move forward together. What is their final velocity?

Explanation:

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, , we can set up the following equation.

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the velocity of the first car is given. Plug in these values and solve for the final velocity.

### Example Question #1 : Understanding Conservation Of Momentum

car strikes a  car at rest from behind. The bumpers lock and they move forward together. If their new final velocity is equal to , what was the initial speed of the first car?

Explanation:

This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, , we can set up the following equation.

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the final velocity is given. Plug in these values and solve for the initial velocity of the first car.

### Example Question #351 : High School Physics

ball moving at  strikes a  ball at rest. After the collision the  ball is moving with a velocity of . What is the velocity of the second ball after the collision?

Explanation:

We can use the law of conservation of momentum:

We know the mass of each ball and their initial velocities.

We also know the final velocity of the first ball. This leaves only one variable: the final velocity of the second ball.

Solve to isolate the variable.

### Example Question #1 : Understanding Conservation Of Momentum

ball moving at  strikes a second ball at rest. After the collision the  ball is moving with a velocity of  and the second ball is moving with a velocity of . What is the mass of the second ball?

Explanation:

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for the mass of the second ball.

### Example Question #5 : Understanding Conservation Of Momentum

ball strikes a second  ball at rest. After the collision the  ball is moving with a velocity of  and the second ball is moving with a velocity of . What is the initial velocity of the first ball?

Explanation:

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy.

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for the initial velocity of the first ball.

### Example Question #1 : Understanding Conservation Of Momentum

A car with mass  and initial velocity  strikes a car of mass , which is at rest. If the two cars stick together after the collision, what is the final velocity?

Explanation:

We know that the cars stick together after the collision, which means that the final velocity will be the same for both of them. Using the formula for conservation of momentum, we can start to set up an equation to solve this problem.

First, we will write the initial momentum.

We know that the second car starts at rest, so this equation can be simplified.

Now we will write out the final momentum. Keep in mind that both cars will have the same velocity!

Set these equations equal to each other and solve to isolate the final velocity.

This is our answer, in terms of the given variables.

### Example Question #11 : Momentum

Two identical billiard balls traveling at the same speed have a head-on collision and rebound.  If the balls had twice the mass, but maintained the same size and speed, how would the rebound be different?

No difference

They would rebound at a higher speed

They would rebound at a slower speed

No difference

Explanation:

Consider the law of conservation of momentum.

If both balls are identical then we can say that

Therefore we can state the equation as

Since  is the common factor we can remove it from the equation completely.

Since mass factors out of the equation; then it does not matter if the balls increase or decrease in their mass.

### Example Question #8 : Understanding Conservation Of Momentum

You are lying in bed and want to shut your bedroom door. You have a bouncy ball and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it?

The blob of clay

Neither will work

Both the same

The bouncy ball

The bouncy ball

Explanation:

A bouncy ball will have an elastic collision with the door, causing the ball to move backward at the same speed it hit the door.

On the other hand, the blob of clay will have an inelastic collision with the door, causing the blob of clay to move with the same speed as the door.

So let us look at the conservation of momentum for an elastic collision.

Since the door has no initial velocity we can remove it from the beginning of the equation.

Since the ball will rebound with the same amount that it hits the door the velocity at the end is a negative of the velocity at the beginning.

Rearrange for the final velocity of the door.

Now let us examine the law of conservation of momentum for the inelastic collision.  Again the door has no initial velocity so we can remove it from the beginning of the equation.

Since the collision is inelastic, the final velocity of both objects will be the same so we can set them equal to each other.

Now solve for the final velocity of the door.

When we compare these two final velocities, it is clear that the elastic collision will create a larger velocity for the door because the top number is twice the value as the inelastic collision, and it is being divided by only the mass of the second object, instead of both objects combined.

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