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What is Impulse? Formula with Real-Life Examples

Jul 12, 2022
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Impulse

You use the concept of impulse in your everyday life without even realising it, for instance, when you hit a punching bag or kick a ball. So, The concept involves a change in the object’s momentum when force is introduced for a specific time. The following article explores this important Physics concept in detail. Learn what is impulse, the formula for calculations, equations, examples and applications.

What is Momentum?

To understand the impulse, you need to know what momentum is. Momentum is mass in motion. It is the product of mass and velocity, given by the following formula:

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p = mv

Where m is the mass in kg and v is the velocity in m/s. The SI unit of momentum is kg m/s or Ns. Since velocity is involved in the calculation of momentum, it is a vector quantity. ​So, an object at rest has zero momentum. Also, momentum is directly proportional to mass and velocity. So, increasing either will increase the momentum. 

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Think about it:

If a bowling ball and ping pong ball have the same velocity, which one would have a greater momentum?

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Hint: p = mv

The formula of momentum can also be written as follows:

Δp =m⋅Δv

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Δp =m⋅a⋅Δt

Δp =F⋅Δt

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So, how does momentum relate to impulse? The following section explains the relationship between the two. 

What is Impulse?

Can you figure out when a force acts on a body for a small duration, how much will the force change the momentum of the body? That is an impulse! It is the measure of this change in the momentum of an object. 

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So, how would you define impulse? 

The change in momentum of a body due to the force acting on it is called impulse. It is the product obtained by multiplying the average value of a force and the time during which it acts.  

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What is the Impulse Formula?

It is denoted by the symbol J. The impulse formula is as follows:

Impulse = Force * Time

J = F⋅Δt 

where Δt is the difference between final and initial time ( final – initial ). 

The SI unit of impulse is Newton-seconds or kg m/s. 

A change in momentum is also given by the same formula as that of impulse:

Δp =F⋅Δt

This equation is also known as the impulse equation. In terms of change in momentum, you can write the alternative formula as follows:  

Δp = p final -p initial

It can also be calculated using the following formula:

Δp = J = mvf – mvi

Where vf represents the final velocity and vi represents the initial velocity. 

You can also calculate the impulsive force using the formula:

F = ma

F = m (vf – vi)/t

Thus, you can conclude that if the impulse is the product of force and time, then force is the impulse divided by time. 

Dimensional Impulse Formula

The standard equation is as follows:

J = F.Δt

Force is measured in Newton, and the dimensional formula for force is [M1L1T-1].

Δt is measured in seconds, and the dimensional formula is [M0L0T1]

Combining the two, the dimensional formula of impulse is as follows:    

= [M1L1T-2] * [M0L0T1]

= [M1L1T-1]

Understanding Impulse with an Example

Example 1: A toy car collides with a wall and stops after the collision. If the mass of the car is 0.5 kg and it was travelling at a velocity of 10 m/s before it hit the wall, what would be the impulse? 

Using the formula: Δp = p final -p initial

Δ p = J = mvf – mvi

J = (0.5 kg)(0 m/s) – (0.5 kg)(10 m/s) 

J = -5 kg m/s

The first example explored a situation where the object comes to rest after collision. The following example presents you with the bouncing back of the object after the collision. 

Example 2: A toy car hits the wall and reverts back after the collision. If the mass of the car is 0.5 kg and it was travelling with a velocity of 10 m/s before it collided with the wall, calculate its impulse when the velocity after the collision is -10 m/s. Note: the negative velocity depicts the motion in the opposite direction. 

Using the formula: Δp = p final -p initial

Δ p = J = mvf – mvi

J= (0.5 kg)(-10 m/s) – (0.5 kg)(10 m/s) 

J = -5 kg m/s – 5 kg m/s 

J = -10 kg m/s

The following example allows you to calculate impulse when force and time are given instead of changing velocities.

Example 3: Calculate impulse caused by an average force of 20 Newtons that acts on a body for 2.0 seconds. 

Impulse = Force * time

J = 20 N * 2 s

J = 40 Ns

When given the initial and final velocity, mass and time, you can calculate the impulsive force experienced by a body, as shown below.

Example 4: Calculate the impulsive force applied to the ball when a player hits it at a speed of 45m/s. Given the bat is in contact with the ball for 3s and the mass of the ball is 50g. 

m = 0.050 kg

vi = 0

vf = 45m/s

t = 3s

Impulse force F = ma = m (vf – vi)/t

F = 0.050 * (45-0)/3

F = 0.050 * 45/3

F = 0.75 kg m/s

Impulse and Variable Force

One of the major reasons why the concept of impulse is important in the real world is that the forces are not always constant. Often forces caused by engines and people build up from zero over time and vary as per the prevailing factors. In such cases, directly working out the overall effect of all forces gets difficult. However, calculating and multiplying force with time is the same as finding the area covered under a force-time curve. So, it gets easier as the area can be calculated for any complicated shape, as in the case of variable force.

Real-Life Examples Impulse

Following are some examples of impulsive force from your day-to-day life:

Football Kicks

When a footballer kicks a football with a sudden force, it shoots away. The velocity of the football is zero when it is at rest. So, the momentum calculated by multiplying the body’s mass and velocity is also zero. As soon as the footballer hits the ball, the momentum increases due to the velocity development. This sudden momentum change generates an impulsive force that allows the ball to travel long distances.

Golf

A golf ball at rest receives a sudden change in momentum as the golfer hits the ball. In a short reaction time, there is a huge development of an impulsive force that helps the ball to cover large distances.

Martial Art

If you have ever come across martial artists, didn’t you find it amazing how they break planks in a swift hand move? A martial artist uses the impulsive force concept as they move their hand swiftly and hit the object at a faster rate. With an increased speed, the reaction time gets significantly reduced, generating a large impulsive force that breaks the hard objects into pieces.

Pestle and Mortar

Mortar and pestle follow the same concept of impulsive force. A pestle exerts a short time force on the spices in a mortar. The force is strong and has a small response time; thus, the objects in the mortar get crushed into smaller pieces.

Egg Carton

The soft-cardboard material of an egg carton is specially designed to save the eggs from coming in contact with any external force. The cardboard helps increase the reaction time, thereby reducing the impulse force, saving the eggs from being broken.

Frequently Asked Questions 

Q1. What is a specific impulse?

It is denoted by Isp, which is given to engines that produce a thrust force. For instance, rocket and jet engines have specific impulses as important specifications. It is a measurement of the efficiency of utilising fuel to produce thrust.

Q2. What is the concept behind airbags in vehicles?

Airbags in vehicles reduce the effect of the force exerted on a person during a collision. They extend the time in which the driver and passenger strike the windshield. So, instead of hitting the windshield, the driver and passenger hit an airbag, the impact time increases and the resultant damage/injury due to force gets reduced. 

Q3. Is impulse vector or scalar?

It is a change in momentum calculated by multiplying mass and velocity. Since velocity is a vector quantity, the impulse is also a vector quantity. It has a direction as well as magnitude. 

Conclusion

Notably, a change in momentum and impulse have the same unit and dimensional formula. The two have the same SI unit Ns or kg.m/s. The concept plays a significant role in deriving suitable protective applications such as car airbags, protective padding in sports, and more. While calculating the impulse, pay attention to the signs as the impulse is a vector quantity and the positive sign indicates forward momentum while the negative sign implies backward movement.

impulse

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