Momentum and Collisions

Momentum and Collisions

High School

​

Learning Objectives

• Calculate and explain what momentum is and how it is determined.

• Calculate and explain impulse and its relationship to a change in momentum.

• Classify and compare the different types of collisions between two objects.

• Explain the law of conservation of momentum and how it applies to collisions.

Key Vocabulary

​

Momentum

A measure of an object's mass in motion, found by multiplying its mass and velocity.

​

Impulse

The change in momentum of an object, which depends on the applied force and time.

​

Elastic Collision

A collision where both total momentum and total kinetic energy of the system are conserved.

​

Inelastic Collision

A collision where momentum is conserved, but kinetic energy is lost as heat or deformation.

​

Conservation of Momentum

The principle that a system's total momentum stays the same before and after a collision.

​

​

What is Momentum?

​

​

Solved Example 1
A bowling ball has a mass of 7 kg and travels down the lane at a velocity of 6 m/s. What is the momentum of the bowling ball?

​

Step 1: Analyze and Sketch the Problem

​

Solved Example 1
A bowling ball has a mass of 7 kg and travels down the lane at a velocity of 6 m/s. What is the momentum of the bowling ball?

​

Step 2: Solve for the Unknown

​

Solved Example 1
A bowling ball has a mass of 7 kg and travels down the lane at a velocity of 6 m/s. What is the momentum of the bowling ball?

​

Step 3: Evaluate the Answer

• The momentum of the bowling ball is 42 kg·m/s.

• The units are correct for momentum, and the answer is reasonable for the given mass and velocity.

Multiple Choice

A 1000-kg car is moving northward at 20 m/s. According to the definition of momentum, what is required to fully describe it?

• Its mass (1000 kg) and speed (20 m/s) only.

• Its acceleration and the distance it has traveled.

• Its mass (1000 kg), speed (20 m/s), and direction (northward).

• The force that set the car in motion only.

​

​

The Law of Conservation of Momentum

​

​

Solved Example 2
A 2 kg ball moving at 5 m/s is about to collide with a stationary 3 kg ball. What is the total momentum of the two-ball system before the collision occurs?

​

Step 1: Analyze and Sketch the Problem

​

Solved Example 2
A 2 kg ball moving at 5 m/s is about to collide with a stationary 3 kg ball. What is the total momentum of the two-ball system before the collision occurs?

​

Step 2: Solve for the Unknown

​

Solved Example 2
A 2 kg ball moving at 5 m/s is about to collide with a stationary 3 kg ball. What is the total momentum of the two-ball system before the collision occurs?

​

Step 3: Evaluate the Answer

• The total momentum is the sum of the momentum of the moving ball (10 kg·m/s) and the stationary ball (0 kg·m/s), which equals 10 kg·m/s.

• This makes sense as only one object is in motion before the collision, and the units of kg·m/s are correct for momentum.

Multiple Choice

In an isolated system, two billiard balls collide and bounce off each other. According to the Law of Conservation of Momentum, what can be said about the total momentum of the system?

• The total momentum decreases because the balls moved in different directions.

• Momentum is not conserved unless the objects stick together.

• The total momentum after the collision is greater than before.

• The total momentum before the collision is equal to the total momentum after the collision.

Impulse and Types of Collisions

​

What is Impulse?

• ​Impulse is the change in an object's momentum over a period.

• ​​It depends on the amount of force and the time applied.

• ​Soft surfaces increase impact time, which reduces the overall force felt.

​

Elastic Collisions

• ​In these collisions, both momentum and kinetic energy are conserved.

• ​​Objects will typically bounce off each other after they make contact.

• ​For example, when two rubber balls happen to collide together.

​

Inelastic Collisions

• ​Momentum is conserved in these collisions, but kinetic energy is not.

• ​​Kinetic energy is changed into other forms like heat or sound.

• ​In some cases, the colliding objects will stick together after impact.

​

Solved Example 3
A 10 kg cart moving at 2 m/s collides with a stationary 5 kg cart. They stick together after the collision. What is the final velocity of the combined carts?

​

Step 1: Analyze and Sketch the Problem

​

Solved Example 3
A 10 kg cart moving at 2 m/s collides with a stationary 5 kg cart. They stick together after the collision. What is the final velocity of the combined carts?

​

Step 2: Solve for the Unknown

​

Solved Example 3
A 10 kg cart moving at 2 m/s collides with a stationary 5 kg cart. They stick together after the collision. What is the final velocity of the combined carts?

​

Step 3: Evaluate the Answer

• The final velocity of approximately 1.33 m/s is less than the initial velocity of the moving cart (2 m/s). This is logical because the initial momentum is now distributed over a larger total mass.

• The direction of the final velocity is the same as the initial direction of the 10 kg cart, and the units (m/s) are correct for velocity.

Multiple Choice

A car rear-ends another, causing deformation, but they do not stick together. Momentum is conserved, but kinetic energy is not. How would you classify this collision?

• Perfectly Inelastic Collision

• An event where momentum was not conserved

• Elastic Collision

• Inelastic Collision

​

Common Misconceptions about Momentum

Multiple Choice

A 1500 kg car's velocity doubles. What is the effect on its momentum, and why?

• The momentum does not change, only the kinetic energy changes.

• The momentum is doubled because momentum is directly proportional to velocity.

• The momentum is quadrupled because momentum is proportional to the square of the velocity.

• The momentum is halved because velocity and momentum are inversely related.

Multiple Choice

How does Newton's Third Law explain the conservation of momentum in a collision between a cue ball and a billiard ball?

• The action-reaction forces are equal and opposite, resulting in a net transfer of momentum with no loss.

• Newton's Third Law does not apply to collisions, only to stationary objects.

• Momentum is lost due to friction, as described by Newton's Third Law.

• The cue ball exerts a greater force, causing momentum to increase.

Multiple Choice

A 70 kg person running at 3 m/s collides with and holds onto a 30 kg stationary cart. Predict the motion of the person and cart after the collision.

• They will move in the opposite direction of the runner's initial motion.

• They will move together in the runner's original direction, but at a slower velocity.

• They will move together at the runner's original velocity of 3 m/s.

• They will remain stationary as the momentum cancels out.

Multiple Choice

Analyze a perfectly inelastic collision versus an elastic collision. If your goal was to absorb the most energy from the impact (e.g., in a car crash), which type of collision would be preferable and why?

• An elastic collision, because kinetic energy is conserved.

• Neither, as the energy absorbed is the same in all collisions.

• An inelastic or perfectly inelastic collision, because kinetic energy is not conserved and is converted to other forms like deformation.

• An elastic collision, because the objects bouncing apart dissipates energy.

​

Summary

Poll

On a scale of 1-4, how confident are you about the concepts covered in today's review?

• 1

• 2

• 3

• 4