Momentum and Collisions Worksheet Answer Key

Momentum and Collisions: Understanding the Fundamentals

Momentum and collisions are fundamental concepts in physics that help us understand how objects move and interact with each other. Momentum is a measure of an object’s mass and velocity, and it plays a crucial role in determining the outcome of collisions. In this worksheet, we will explore the key concepts and formulas related to momentum and collisions, and provide answers to common problems.

What is Momentum?

Momentum is a vector quantity that depends on an object’s mass and velocity. The momentum of an object can be calculated using the following formula:

p = mv

where:

• p is the momentum of the object
• m is the mass of the object
• v is the velocity of the object

The unit of momentum is typically measured in kilogram-meters per second (kg·m/s).

Types of Collisions

There are two main types of collisions: elastic and inelastic. In an elastic collision, the total kinetic energy of the system is conserved, and the objects involved in the collision do not lose any energy. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

Conservation of Momentum

The law of conservation of momentum states that the total momentum of a closed system remains constant over time. This means that if two objects collide, the total momentum before the collision is equal to the total momentum after the collision.

p1 + p2 = p1’ + p2’

where:

• p1 and p2 are the momenta of the objects before the collision
• p1’ and p2’ are the momenta of the objects after the collision

Example Problems and Solutions

Problem 1

A 2 kg object is moving at a velocity of 3 m/s. What is its momentum?

Solution

p = mv = 2 kg × 3 m/s = 6 kg·m/s

Problem 2

A 5 kg object is moving at a velocity of 2 m/s, and it collides with a 3 kg object that is moving at a velocity of 4 m/s. What is the total momentum of the system before and after the collision?

Solution

Before collision:

p1 = 5 kg × 2 m/s = 10 kg·m/s p2 = 3 kg × 4 m/s = 12 kg·m/s Total momentum = p1 + p2 = 10 kg·m/s + 12 kg·m/s = 22 kg·m/s

After collision:

Let’s assume the objects stick together after the collision. The total momentum after the collision is still 22 kg·m/s.

Problem 3

A car with a mass of 1500 kg is traveling at a velocity of 25 m/s. If it collides with a wall and comes to rest, what is the impulse exerted on the car?

Solution

The impulse exerted on the car is equal to the change in its momentum.

J = Δp = p2 - p1 = 0 - (1500 kg × 25 m/s) = -37500 N·s

The negative sign indicates that the impulse is opposite to the direction of the car’s velocity.

🔍 Note: Impulse is a measure of the change in momentum, and it is often denoted by the symbol J.

As we have seen, momentum and collisions are fundamental concepts in physics that help us understand how objects move and interact with each other. By applying the formulas and concepts outlined in this worksheet, you can solve a wide range of problems related to momentum and collisions.

Momentum and collisions are all around us, from the simplest interactions between objects to the most complex phenomena in the universe. By understanding these concepts, we can gain a deeper appreciation for the world around us and develop new technologies and innovations that transform our lives.