# What is Impulse?

Last Updated : 20 Jun, 2023

Impulse in Physics is defined as the force acting on the body for a very shorter period of time. It is the instant change in the momentum of the body. For example, in case of collision, the instant change in the momentum of the body just before and after the collision is called the Impulse acting on the body.

The damage sustained by the body is dependent on the impulse applied to the body. It is denoted using the letter ‘J’ and is calculated by taking the product of the force applied and the time for which the force is applied.

## Momentum

Momentum is a physical quantity given by product of the mass of the body and its velocity. It is given as p = mv. Its unit is kgm/s.

Physically momentum means the strength of a moving body that can cause an impact on another body. Furthermore, a stable or motionless object has no or zero motion, this means its momentum is zero and can’t impact on another body. Moreover, a huge, slow-moving item has significant momentum, as does a tiny, fast-moving item. A force can influence an object’s velocity in either direction. In addition, if the object’s velocity varies, the momentum changes as well.

In athletics, the term “momentum” is frequently used. When a pundit states that a player has momentum, it signifies that the person is genuinely moving and that stopping him or her is extremely tough. Because a body with momentum cannot be halted, it is necessary to exert a force against its direction of motion for a certain amount of time. The more momentum there is, the more it is difficult to halt. As a result, a greater amount of power is necessary, as well as a significant length of time to bring the body to a complete stop. The body’s velocity varies as force works on it for a specific period of time, and therefore the body’s momentum changes.

### Momentum Formula

The formula for the momentum of any object is given as:

p = mv

where,
m is the mass of object
p is the momentum
v is the velocity of object.

Furthermore, momentum is a vector that equals the product of the velocity vector and mass. But what is the relationship between impulse and momentum? When a force operates on an item for a brief period of time, the measure of how much the force modifies the item’s momentum is called impulse.

## Impulse Definition

When a net force acts on a body, it causes acceleration, which changes the body’s motion. A larger net force will result in greater acceleration than a small net force. If the big and tiny forces occur at different time periods, the overall change in motion of the item might be the same. The combination of force and time acts as a valuable quantity leading to the definition of impulse.

The product of the average net force acting on an item for a certain period of time is sometimes referred to as the impulse.

### Impulse Formula

Impulse is a vector quantity and the formula for impulse is given using the formula,

J = F × Δt

where,
J is the impulse
Δt is the time interval
F is the force.

It’s worth noting that we assume force remains constant throughout time. Like force, the impulse is a vector quantity with a direction.

## Impulse-Momentum Theorem

A person must know the mechanics of collisions. The laws of momentum and the first law (known as the change in impulse equation) govern collisions. In a collision, the body is subjected to a force for a specific amount of time, resulting in a change in momentum. The body either slows down, speeds up, or changes direction as a result of a force acting for a certain length of time.

In a collision, the item receives an impulse that is equivalent to a change in momentum. Consider a footballer who is sprinting down the field when he collides with a defensive back. The halfback’s pace and momentum change as a result of the contact.

The impulse-Momentum theorem aids in the understanding of these two concepts. The theorem simply asserts that the change in an object’s momentum is proportional to the amount of impulse applied to it.

The alternate formula of impulse is given as:

J = Δp = pf  −  pi

where,
Δp is the change in momentum
pf is the final momentum
pi is the initial momentum

Since, mass of the object remains constant, it can also be given as:

J = m × (vf − vi)

where,
m is mass of the object
vf is the final velocity
vi is the initial velocity

Most importantly, the formula correlates impulse to the object’s change in momentum. In addition, impulse can be measured in kilogram meters per second (kg m/s) or Newton times seconds (Ns).

## How to Calculate Impulse?

The impulse acting on any object is calculated using the Impule formula as discussed above. Follow the following steps to calculate the Impulse acting on the object.

Step 1: Note the Momentum of the object just before the collision, and the momentum of the object just after the collision.

Step 2: Find the change in momentum of the object by taking the difference between the final momentum and the initial momentum.

Step 3: Use the Impulse formula

(Impulse) J = Δp(change in momentum)

Step 4: Simplify the value obtained in step 3 to get the final answer.

Example: A kicks a ball rolling at 6 m/s after the kick the ball attains a velocity of 36 m/s. Find the impulse applied to the ball if the mass of the ball is 1/2 kg.

Solution:

We know that the Impulse formula is,

J = Δp

Given,
mass of ball (m) = 1/2 kg
Initial velocity of Ball (vi) = 6 m/s
Final velocity of Ball (vi) = 36 m/s

Initial Momentum = mvi = 1/2×6 = 3 kgm/s

Final Momentum = mvf = 1/2×36 = 18 kgm/s

Impulse (J) = mvf – mv = 18 – 3 = 15 kgm/s

Thus, the Impulse applied to the ball is 15 kgm/s

## Newton’s Second Law

The relationship between Impulse and Newton’s Law of Motion is very crucial. Newton’s second law is very useful for finding the value of the Impulse.

We know that force acting on an object is given using,

F = ma

We know that acceleration (a = △v/△t)

F = m(△v/△t)

F△t = m△v

F△t = m(vf − vi)

where the quantity F△t implies that Impulse acting on the body and it is given as the change in linear momentum of the body.

This concept can be explained using the case of collision. In case of a collision large force is applied to a body if we reduce the time for the impact of the collision the impulse acting on the body is reduced drastically and thus the impact of the collision is lower.

## Impulse Examples

A few examples of impulse are given below,

• When someone falls from a bed onto a floor, they sustain more damage than if they fall onto a heap of sand. This occurs because the sand yields more than the cemented floor, increasing the contact time and reducing the force effect.
• For the same reason, nylon ropes are utilized in the sport of rock climbing. Climbers use nylon ropes to secure themselves to the rock faces. A rock climber will start to tumble if she loses her grasp on the rock. In this case, her speed will be eventually slowed by the rope, averting a dangerous fall to the ground below.
• Hitters are frequently instructed to follow through while striking a ball in racket and bat sports. High-speed videos of the collisions between bats/rackets and balls have indicated that the act of following through serves to lengthen the duration over which a collision occurs. In the impulse-momentum change theorem, this increase in time must result in a change in another variable.

## Solved Examples on Impulse

Example 1: An item comes to a halt when it collides with a solid wall. Calculate the object’s impulse if the object was 2.0 kg in weight and travelled at a speed of 10 m/s before colliding with the wall.

Solution:

Given,

Mass of the object, m = 2.0 kg

Initial velocity of the ball, vi = 10 m/s

Final velocity of the ball, vf = 0 m/s

The formula for impulse is:

J = m × (vf − vi)

Substitute all the values in the above equation.

J = 2 × (0 – 10) kg m/s

= -20 kg m/s

Hence, the impulse on the object is -20 kg m/s.

Example 2: A golfer hits a ball of mass 100 g at a speed of 50 m/s. The golf club is in contact with the ball for 2 ms. Compute the average force applied by the club on the ball.

Solution:

Given,

Change in the velocity, Δv = 50 m/s

Mass of the ball, m = 100 g = 0.1 kg

Time of contact, t = 2 ms = 0.002 s

The formula of impulse is:

J = F × Δt = m × Δv

F = m × Δv / Δt

Substitute all the values in the above equation.

F = (0.1) × (50) / 0.002 N

= 2500 N

Hence, the average force applied on the ball is 2500 N.

Example 3: Calculate the impulse on a body hit by a force of 500 N with a time of contact equal to 0.1s.

Solution:

Given,

Force exerted on body, F = 500 N

Time of contact, Δt = 0.1 s

Formula for impulse is,

J = F × Δt

=(500) × (0.1) N s

= 50 N s

Hence, the impulse on body is 50 N s.

## FAQs on Impulse

### Q1: What is Impulse?

Impulse is defined as the product of the force applied and the time interval for which the force acts on the body. It is calculated using the formula, J = F × Δt.

### Q2: What is the Unit of Impulse?

As we know that impulse is calculated using the formula J = F × Δt. Its SI unit is Newton-Second.

### Q3: How Impulse is related to Momentum?

The change in linear momentum of the body is equal to the Impulse of the body,

J = ΔP

### Q4: What is Impulse Dimensional Formula?

The dimensional formula for the impulse is [MLT-1]