Impulse Formula

Impulse is something that you use occasionally or daily. Furthermore, it is a concept that we use whenever we hit a ball. Besides, in this topic, we will discuss impulse, Impulse formula, derivation of impulse formula, and solved example. Also, we will learn about the connection amidst momentum and impulse.

Impulse

In our daily life, we have kicked a ball, hit a punching bag, and played sports that involve any kind of ball, etc. in all these things we use impulse without knowing it. Hence, the question here is what is impulse and what it has to do with these situations?

Before discussing impulse we first need to converse about the concept of momentum. Momentum refers to the measure of strength. Also, it is a measure of how difficult it is to stop an object. Moreover, an object that is stable or stationary has no or zero momentum. Besides, a slow-moving large object has large momentum also, a small but fast-moving object has a large momentum.

As an example, suppose a Bowling ball and Ping-Pong ball have the same velocity, then the Bowling ball will have greater momentum because it is bigger than the Ping-Pong ball.

Momentum Formula

The formula of momentum is
\(\vec{p}\) = \(m\vec{v}\)

Derivation of the Formula

\(\vec{p}\) = refers to the momentum
m = refers to the mass of the object
\(\vec{v}\) = refers to the time velocity of the object

Besides, momentum is a vector that is equal to the product of the mass and velocity (also a vector).

But, the question is how impulse relates to momentum? The answer is that when a force acts on an object for a short period of time then impulse is the measure of how much the force changes the momentum of an object.

Impulse Formula

Impulse = Force × (final time – initial time)
Impulse = Force × \(\Delta t\)
I = F × \(\Delta t\)

Derivation of the Formula

I = refers to the impulse
F = refers to the force of the object
\(\Delta t\) = refers to the change in time

Since the impulse is a measure of how much the momentum changes as a result of a force acting on it for a period of time. Moreover, an alternative formula for impulse is

Impulse = \(\Delta \vec{p}\) = \(\vec {p}_{final}\) – \( \vec{p}_{initial}\)

Derivation

\(\Delta \vec{p}\) = refers to the change in momentum
\(\vec {p}_{final}\) = refers to the final momentum
\(\vec{p}_{initial}\) = refers to the initial momentum

Most noteworthy, the formula relates impulse to the change in the momentum of the object. Also, impulse has two different units, it can either kilogram meter per second (kg m/s) or Newton times seconds (Ns).

Solved Example on Impulse Formula

Example 1

An object collides with a solid wall and after the collision, it stops. Now. If the wright of the object was 2.0 kg and the object travels with a velocity of 10 m/s before it hit the wall. Calculate the impulse of the object.

Solution:

\(\Delta p\) = \(p_{f}\) – \(p_{i}\)
\(\Delta p\) = m \(v_{f}\) – m \(v_{i}\)
\(\Delta p\) = (2.0 kg)(0 m/s) – (2.0 kg) (10 m/s)
\(\Delta p\) = -20 kg m/s

Example 2

In this example, the object first collides with the wall and then bounce back. Furthermore, before hitting the wall, the mass of the object is 2.0 kg and its velocity is 10 m/s. Moreover, after hitting the wall its velocity becomes -10 m/s (it is negative because it has bounced back in the opposite direction). Now, calculate the impulse of the object.

Solution:

\(\Delta p\) = \(p_{f}\) – \(p_{i}\)
\(\Delta p\) = m \(v_{f}\) – m \(v_{i}\)
\(\Delta p\) = (2.0 kg)(-10 m/s) – (2.0 kg) (10 m/s)
\(\Delta p\) = -20 kg m/s -20 kg m/s
\(\Delta p\) = -40 kg m/s