Grade 8

Intermediate

7 min

Lesson 10 of 12

Introduction to Momentum

Not Started

Understanding 'mass in motion' and how it relates to Newton's Laws.

Why can a tiny bullet cause more damage than a slow-moving car, even though the car is thousands of times heavier? The answer lies in a hidden physical power called momentum.

Learning Objectives

1.Define momentum and identify its two main factors: mass and velocity.
2.Calculate the momentum of an object using the formula $p = m \cdot v$ .
3.Explain how force and time work together to change an object's motion.

What is Momentum?

In physics, momentum is often described as 'mass in motion.' Every moving object has momentum, but an object at rest has none. Two factors determine how much momentum an object possesses: its mass ( $m$ ) and its velocity ( $v$ ). Because velocity includes direction, momentum is a vector quantity, meaning it always points in the same direction as the object's motion. The standard unit for momentum is the kilogram-meter per second ( $kg \cdot m/s$ ). If you increase either the mass or the speed of an object, you increase its momentum, making it harder to stop.

Let's calculate the momentum of a standard bowling ball.

1. Identify the mass: $m = 5 kg$ . 2. Identify the velocity: $v = 3 m/s$ to the right. 3. Use the formula: $p = m \cdot v$ . 4. Calculate: $p = 5 kg \cdot 3 m/s = 15 kg \cdot m/s$ to the right.

Quick Check

If a truck and a fly are both moving at exactly 10 m/s, which one has more momentum?

Look at the formula

p = m \cdot v

. If

v

is the same, how does

m

affect

p

Answer

The truck has more momentum because it has a much larger mass.

The Momentum Formula

To find the exact value of momentum, we use the equation:

p = m \cdot v

where

p

represents momentum,

m

is mass in kilograms, and

v

is velocity in meters per second. This relationship is linear, meaning if you double the mass of an object while keeping its speed the same, you exactly double its momentum. Similarly, a car traveling at

20 m/s

has twice the momentum of the same car traveling at

10 m/s

. This is why speed limits are so important; higher speeds result in much higher momentum, which requires more effort to stop during an emergency.

Which has more momentum: a $1,000 kg$ car moving at $20 m/s$ or a $2,000 kg$ truck moving at $10 m/s$ ?

1. Car: $p = 1,000 kg \cdot 20 m/s = 20,000 kg \cdot m/s$ . 2. Truck: $p = 2,000 kg \cdot 10 m/s = 20,000 kg \cdot m/s$ . 3. Result: They have the exact same momentum! The truck's extra mass is perfectly balanced by the car's extra speed.

Quick Check

What is the momentum of a 5,000 kg mountain that is not moving?

Check the definition of 'mass in motion'.

Answer

Zero. If velocity is $0 m/s$ , then $p = m \cdot 0 = 0$ .

Changing Momentum: Impulse

Newton's Second Law tells us that to change an object's motion, we must apply a force. In terms of momentum, the change in momentum (

\Delta p

) depends on how much force you apply and for how long you apply it. This is called Impulse. The formula is:

F \cdot \Delta t = \Delta p

This explains why cars have 'crumple zones' and airbags. By increasing the time (

\Delta t

) it takes for a car to stop during a crash, the force (

F

) felt by the passengers is significantly reduced, even though the total change in momentum is the same.

A $0.5 kg$ soccer ball kicks toward a goalie at $20 m/s$ . The goalie catches it and brings it to a stop in $0.1$ seconds. How much force did the goalie apply?

1. Initial momentum: $p = 0.5 kg \cdot 20 m/s = 10 kg \cdot m/s$ . 2. Final momentum: $0 kg \cdot m/s$ (stopped). 3. Change in momentum ( $\Delta p$ ): $10 kg \cdot m/s$ . 4. Use $F \cdot \Delta t = \Delta p$ : $F \cdot 0.1 s = 10 kg \cdot m/s$ . 5. Solve for $F$ : $F = 10 / 0.1 = 100 N$ .

Key Takeaways

1Momentum is 'mass in motion,' calculated as $p = m \cdot v$ .
2An object must be moving to have momentum; if $v = 0$ , then $p = 0$ .
3Momentum is a vector, meaning it has both a magnitude and a specific direction.
4To change momentum, you must apply a force over a period of time ( $F \cdot \Delta t$ ).

Quick Check

Multiple Choice

What are the two variables that determine an object's momentum?

Multiple Choice

If you triple the velocity of an object without changing its mass, what happens to its momentum?

True/False

An airbag protects you in a crash by increasing the time it takes for your momentum to reach zero.

What's Next?

Review Tomorrow

Tomorrow morning, try to explain to a friend why a heavy boat is harder to stop than a small jet ski, even if they are going the same speed. Use the word 'momentum' and the formula $p=mv$ .

Practice Activity

Find three moving objects today (a car, a person walking, a bird) and estimate which one has the highest momentum based on their relative mass and speed.

Browse

Browse

Introduction to Momentum

Learning Objectives

What is Momentum?

The Momentum Formula

Changing Momentum: Impulse

Key Takeaways

Quick Check

What's Next?

Introduction to Momentum

Learning Objectives

What is Momentum?

The Momentum Formula

Changing Momentum: Impulse

Key Takeaways

Quick Check

What's Next?