Impulse: Definition, Equation, Calculation & Examples

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  • 0:01 Definition of Impulse
  • 1:39 Examples of Impulse
  • 3:19 Applications of Impulse
  • 5:21 Lesson Summary
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Lesson Transcript
Instructor: Richard Cardenas

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

In this lesson you will learn about the concept of impulse and how you can apply it to a variety of interesting situations. You will learn about the relationship between impulse and momentum and how to calculate impulse through a variety of examples.

Definition of Impulse

If you've ever kicked a ball, hit a punching bag, or played sports that involved any kind of ball, you have been using the concept of impulse without even knowing it. So what exactly is impulse, and what does it have to do with any of those situations?

Before we can define impulse, we need to talk about the concept of momentum. Momentum is a measure of strength and a measure of how difficult it is to stop an object. An object that is not moving has zero momentum. A slow-moving, large object has a large momentum. A fast-moving, small object also has a large momentum. For example, if a ping-pong ball and a bowling ball have the same velocity, then the bowling ball has a greater momentum because it is more massive than the ping-pong ball.

This is the formula for momentum:


In this formula, Momentum (p) equals Mass (m) times Velocity (v). Momentum is a vector which is equal to the product of mass and velocity (which is also a vector).

But how is momentum related to impulse? When a force acts on an object for a short amount of time, impulse is the measure of how much the force changes the momentum of an object.

The formula for impulse looks like this:


Because impulse is a measure of how much the momentum changes as a result of force acting on it for a period of time, an alternative formula for impulse looks like this:


This formula relates impulse to the change in the momentum of the object. Impulse has two different units, either kilogram times meters per second (kg m/s) or Newton times seconds (Ns).

Examples of Impulse

Let's take a look at a few examples.

In this first example, we'll look at the impulse for an object that collides with a wall and stops after the collision. If the 2.0 kg object travels with a velocity of 10 m/s before it hits the wall, then the impulse can be calculated.

Δ p = p f - p i

Δ p = m v f - m v i

Δ p = (2.0 kg)(0 m/s) - (2.0 kg)(10 m/s) = -20 kg m/s

Impulse Example 1

In this second example, we'll look at the impulse for an object that collides with a wall and bounces back after the collision. If the 2.0 kg object travels with a velocity of 10 m/s before it hits the wall and a velocity of -10 m/s after the collision (negative because it bounces back in the opposite direction), then the impulse can be calculated as follows:

Δ p = p f - p i

Δ p = m v f - m v i

Δ p = (2.0 kg)(-10 m/s) - (2.0 kg)(10 m/s) = -20 kg m/s - 20 kg m/s = -40 kg m/s

Impulse Example 2

In this next example, we'll calculate impulse a different way. What is the impulse caused by an average force of 10 Newtons if it acts on a ball for 2.0 seconds? The impulse here can be calculated as:

Impulse Example 2 Equation

Applications of Impulse

Now that we can calculate impulse, we can take a look at some interesting examples of impulse in everyday life. The most notable example is the car air bag system. Airbags are in cars in order to reduce the damage to a driver or passenger during a collision.

If impulse is force multiplied by time, then force is impulse divided by time. What the airbag does is increase the time required to stop the momentum of the passenger or driver. If this time is increased, then the force of impact is decreased. If the impact time is short, then the force of impact increases and may cause severe damage to the occupants of the car.

Having padded floors at a gymnasium is another application of the concept of impulse. In order to reduce the force of impact when someone lands on the floor, the padding increases the contact time between the person and the floor. So just like the airbags, when the contact time increases, the impact force decreases.

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