Kinematics-Laws of Motion-Impulse

Impulse

Impulse is the total force that acts on a body at a given time, changing the momentum of that object. Force is a vector quantity (a quantity having both magnitude and direction); thus, impulse is also a vector quantity. The effect of the force of an object is directly proportional to the amount of time the force acts on the object.

Let’s take an example for a better understanding. In martial arts, while braking hard objects, a person uses their hands. They increase the speed to hit the object at a faster rate swiftly. This increase in speed reduces the reaction time. As a result, an impulsive force of a very huge magnitude develops. Therefore, this force is sufficient for breaking objects like wooden sticks or bricks with hands.

As already discussed, impulse and momentum are interlinked; therefore, let’s understand momentum first.

Momentum 

Momentum in physics is the product of the mass of a particle to its velocity. It is a vector quantity with a unit kilogram metre per second (kg. m/s) and is a very common term used in sports. If the momentum is greater, a greater amount of force is needed to stop the moving object. This force affects the velocity of the object too. In a closed system (system with no exchange of matter), the momentum remains constant as long as there is no external force.

The momentum is:

p= mv

where m= mass of the object

v= velocity

We can write, Δv (velocity) is as aΔt in the kinematic equation. 

Thus, the equation will be:

p= mΔv

p=m.a.Δt [F=ma]

p=FΔt

What is Impulse?

As already mentioned, impulse is the product of total force that acts on a body at a given time, changing the momentum of that object. The impulse is represented by the English alphabet J. It helps in better understanding the conservation of momentum and is highly significant in other fields of physics too. The impulse formula is as follows:

J= F. Δt

What is an Impulse Momentum Theorem?

The Impulse-Momentum theorem states that a body experiencing an impulse is equal to its change of momentum. This clearly shows the connection of impulse with momentum.

ΔtF=m (vf) –m (vi)

Where m (vi)= initial momentum

And m (vf)= final momentum

If the mass of initial and final momentum remains unchanged, the Impulse-Momentum equation shall be:

ΔtF=m (vf – vi).

Solved Questions on Impulse

Q 1- The average force acting on a soccer ball for 0.04 s is 200 N. The ball weighs 145g. find the magnitude of impulse acting on the soccer ball.

Solution:

Assume the impulse as I, force as F, and time as t. Thus, to determine the impulse, we get the formula as:

I= Ft

According to the question, F= 200N,

t= 0.04 s.

On substituting the values in the equation I= Ft, we get:

I = 200 × 0.04

=8 Ns (Ns is the unit of Impulse, i.e. the combined unit of force and time).

Q 2- A child throws a cricket ball with a velocity of 4m/s to the left on his garden wall. The ball weighs 20gm, and after colliding the wall, it comes back with another velocity of 2m/s towards the right. What will be the impulse of it?

Solution:

According to question,

Mass (m) = 20 gram

 = 0.020 kg (1kg=1000gm)

Velocity before collision (vo) = -4 m/s (as it is to the left)

Velocity after collision (vt) = +2 m/s (as it is to the right)

To determine the Impulse (I) = the change in momentum (ΔP), i.e.

 ΔP= m vt – m vo

I = m (vt – vo) 

I = 0.02 (2 – (-4))

I = 0.02 (2 + 4)

I = 0.02 ×6

I =0.12 N/s.

Thus, the impulse acting on the ball will be 0.12 N/s. 

Q 3- A ball of mass 4 kg is travelling towards the east at a velocity of 8m/s. Any impulse at point O changes the direction and velocity of the ball towards the north at 6m/s. Find this impulse and the change of momentum too.

Solution: Initial momentum,

P1= m.V1

P1= 4kg×8m/s

P1= 32kg.m/s

Final momentum, 

P2= m.V2

P2= 4kg×6m/s

P2= 24kg.m/s

Total momentum, ΔP=P2+P1 

i.e. ΔP2=P22+P12=m2(v22+v12)

ΔP2=16.100

ΔP=40kg.m/s

As we know that Impulse=change in momentum

I (impulse)=ΔP( change in momentum)=40kg.m/s

Conclusion

Impulse is the total force that acts on a body at a given time, changing the momentum of that object. Force is a vector quantity (a quantity having both magnitude and direction); thus, impulse is also a vector quantity. The effect of the force of an object is directly proportional to the amount of time the force acts on the object.

The impulse is represented by the English alphabet J. It helps in better understanding of conservation of momentum and is highly significant in other fields of physics too. The impulse formula is as follows: J= F. Δt. The Impulse-Momentum theorem states that a body experiencing an impulse is equal to its change of momentum.