### All High School Physics Resources

## Example Questions

### Example Question #1 : Calculating Momentum

A crate slides along the floor for before stopping. If it was initially moving with a velocity of , what is the force of friction?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: . We can rewrite this equation in terms of force.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the object is not moving at the end, its final velocity is zero. Plug in the given values and solve for the force.

We would expect the answer to be negative because the force of friction acts in the direction opposite to the initial velocity.

### Example Question #2 : Calculating Momentum

A hammer moving with a velocity of strikes a nail. The two are in contact for , after which the hammer has a velocity of . With how much force did the hammer strike the nail?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: . We can rewrite this equation in terms of force.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the hammer is not moving at the end, its final velocity is zero. Plug in the given values and solve for the force.

This equation solves for the force of the nail on the hammer, as we were looking purely at the momentum of the hammer.

According to Newton's third law, . This means that if the nail exerts of force on the hammer, then the hammer must exert of force on the nail.

Our answer will be .

### Example Question #1 : Calculating Momentum

A crate slides along a floor with a starting velocity of . If the force due to friction is , how long will it take for the box to come to rest?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Remember that momentum is equal to mass times velocity: . We can rewrite this equation in terms of force.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the box is not moving at the end, its final velocity is zero. Plug in the given values and solve for the time.

### Example Question #4 : Calculating Momentum

A ball strikes a piece of paper moving at . It breaks through the paper and continues on in the same direction. If the paper exerted a force of on the ball and the two are in contact for , what is the final momentum of the ball?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Since we're looking for , we're going to leave that part alone in the problem, but we can expand the rest.

From here, plug in the given values and solve for the final momentum.

At this point, remember that , so sides are now working in the same units.

### Example Question #1 : Calculating Momentum

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

**Possible Answers:**

**Correct answer:**

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 initial velocity of the first car.

### Example Question #6 : Calculating Momentum

Susan pushes a car with of force. How long does she need to push it to get it to a velocity of if it starts at rest and there is no friction?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the car starts from rest, its initial velocity is zero. Plug in the given values and solve for the time.

### Example Question #1 : Calculating Momentum

A hammer moving with a velocity of strikes a nail, after which the hammer has a velocity of . If the hammer strikes the nail with of force, how long were the two in contact?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the hammer is not moving at the end, its final velocity is zero.

The problem gave us the force of the hammer on the nail, but not the force of the nail on the hammer, which is what we need for the equation as we are looking purely at the momentum of the hammer. Fortunately, Newton's third law can help us. It states that . This means that if the hammer exerts of force on the nail, then the nail must exert of force on the hammer.

We can plug that value in for the force and solve for the time.

### Example Question #8 : Calculating Momentum

A hammer moving with a velocity of strikes a nail, after which the hammer has a velocity of . If the hammer strikes the nail with of force, how long were the two in contact?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the hammer is not moving at the end, its final velocity is zero.

The problem gave us the force of the hammer on the nail, but not the force of the nail on the hammer, which is what we need as we are looking purely at the momentum of the hammer.

Fortunately, Newton's third law can help us. It states that . This means that if the hammer exerts of force on the nail, then the nail must exert of force on the hammer.

We can plug that value in for the force and solve.

### Example Question #1 : Calculating Momentum

A crate slides along the floor for before stopping. If it was initially moving with a velocity of , what is the force of friction?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the crate is not moving at the end, its final velocity is zero. Plug in the given values and solve for the force.

### Example Question #1 : Calculating Momentum

A hammer moving with a velocity of strikes a nail. The two are in contact for , after which the hammer has a velocity of . How much force went into the nail?

**Possible Answers:**

**Correct answer:**

The fastest way to solve a problem like this is with momentum.

Using this transformation, we can see that momentum is also equal to force times time.

can also be thought of as .

Expand this equation to include our given values.

Since the hammer is not moving at the end, its final velocity is zero. Plug in the given values and solve for the force.

This equation solves for the force of the nail on the hammer, as we were looking purely at the momentum of the hammer; however, we need to find the force of the hammer on the nail. Newton's third law states that .

This means that if the nail exerts of force on the hammer, then the hammer must exert of force on the nail; therefore, our answer will be .

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