## An Introduction to Impulse

When we hit a punching bag, the punching bag’s momentum changes due to the force applied by our hand for a specific time. This is an impulse. So, we can define impulse as the change in momentum of an object due to a sudden force applied on it for some time. The graph of impulse against time is Gaussian in nature.

## Impulse Meaning

Impulse is the change in momentum of an object due to a force applied on it for some time. The graph of impulse against time is Gaussian in nature. We can see that in the diagram below.

Force Versus Time Graph Depicting the Impulse of the Object.

Impulse can be expressed as the integral of resultant force over the interval of time for which it acts. As the force is a vector quantity, Impulse also becomes a vector quantity having direction and magnitude too.

We have seen that impulse is an integral force over time, and the impulse symbol is ‘J’.

Therefore, we can write \[J = \int {Fdt} \].

## Impulse Momentum Theorem

Impulse acting on a body is equal to the change in linear momentum.

We saw impulse as \[J = \int {Fdt} \]

Between time interval t1 and t2, we can write

\[J = \int\limits_{{t_1}}^{{t_2}} {Fdt} \]

But \[F = \dfrac{{dp}}{{dt}}\], substituting in above equation, we get,

\[J = \int\limits_{{t_1}}^{{t_2}} {\dfrac{{dp}}{{dt}}dt} \]

This becomes \[J = \int\limits_{{P_1}}^{{P_2}} {dp} \]

which is equal to \[J = {p_2} - {p_1} = \Delta p\].

This is the equation of impulse momentum theorem.

## SI Unit of Impulse

Impulse units can be derived from the impulse momentum theorem. Impulse momentum theorem is given as \[J = {p_2} - {p_1} = \Delta p\].

\[\begin{array}{l}p = m\upsilon \\J = \Delta p = m\Delta \upsilon = kgm/s\\\end{array}\]

But

\[\begin{array}{l}kgm/{s^2} = N\\\therefore kgm/s = N.s\end{array}\].

Therefore, the SI unit of J - Impulse becomes N.s and the equivalent unit is kgm/s.

## Interesting Facts

Airbags for safety in our cars are designed on the principle of impulse.

Tossing the coin is an example of impulse.

Kick starting a bike is an example of impulse.

## Practice Question

What is meant by impulse? Give one example.

Impulse is the change in momentum of an object due to a force applied on it for some time. An example is when we hit a punching bag, punching bag’s momentum changes due to the force applied by our hand for a specific time. This is an impulse.

## Solved Problems

Consider a free-falling mass of 0.5kg falling from a height h1=7m and is reflected at a height h2 = 3m. Find impulse (take g=10).

Solution: Given,

m= 0.5kg

h1=7m

h2=3m

g=10m/s2

Velocity before collision:

For free falling body \[{\upsilon ^2} = 2gh\]

\[\therefore {\upsilon _0}^2 = 2 \times 10 \times 7 = 140\]

\[\therefore {\upsilon _0} = \sqrt {140} = - 11.8m/s\]

Negative sign indicates direction of object.

Velocity after collision:

\[{\upsilon _t}^2 = {\upsilon _0}^2 + 2gh\]

\[0 = {\upsilon _0}^2 + (2 \times - 10 \times 3)\]

\[{\upsilon _0}^2 = 60\]

\[{\upsilon _0} = \sqrt {60 = } 7.74m/s\]

We know that \[J = {p_2} - {p_1} = \Delta p\].

\[\therefore J = m({\upsilon _t} - {\upsilon _0}) = 0.5 \times (7.74 + 11.8) = 9.77N.s\]

Consider a free-falling ball of mass 0.5kg strikes the floor. Velocity before the collision is 5m/s and velocity after the collision is 3m/s. Find impulse.

Solution: Given,

m=0.5kg

V0=-5m/s

Vt=3m/s

We know that \[J = {p_2} - {p_1} = \Delta p\]

\[\therefore J = m({\upsilon _t} - {\upsilon _0}) = 0.5 \times (3 - ( - 5)) = 4N.s\]

## Summary

Impulse is the change in momentum of an object due to a sudden force applied on it for some time. The SI unit of impulse is N.s. Impulse is shown by the symbol ‘J’. Impulse is a vector quantity; it has direction and it also has magnitude. Punching a punching bag is a real-life example of impulse.

## FAQs on Impulse Units

1. What is linear momentum?

Linear moment is defined as the product of mass and velocity. It is a vector quantity. ‘p’ is the symbol of linear momentum. The direction of momentum is always the same as the direction of velocity. Linear momentum is a conserved quantity. The unit of linear momentum is kg m/s. Linear momentum is given by the formula p=m*v. The rate of change of the linear momentum of the body is equal to the net force applied to the body which can be given by equation \[F = \dfrac{{dp}}{{dt}}\].

2. What is the difference between the impulse and impulsive force?

Impulse can be simply defined as a product of the force and the time period of force applied. Solid state rocket engines work that way. Unit of impulse is Newton-seconds. When we light an engine, it burns for a time with a propulsive force. Impulse unit N-s has the same dimension as momentum. This way we can say that the engine will give the rocket the momentum of mV. Light rockets go faster than heavy rockets. Impulsive force is the force acting on the body for a short interval of time. It can be defined as the rate of change of momentum of the body during the interval of application of force.

3. What is the difference between impulse and momentum?

Impulse: Impulse is a measure of force that acts for a very short duration. It is represented as the product of the force applied (F) and the time (t, which is very small). For example, when a batsman hits a cricket ball, the force applied by the batsman acts for a very short duration on the ball.

Impulse = force × time

Momentum: Momentum is an indicator of the amount of motion any body possesses. It is represented as a product of the object's mass (m) and velocity (v).

Momentum = mass x velocity