Impulse

As we already mentioned, the impulse is the amount or quantity of force acting on a certain body in a given time that changes its momentum. The amount of effect a force brings is directly proportional to the duration of time the force acts. Force and impulse are both vectors (quantity with both magnitude and direction). For example, the player kicks the ball with force during a football match. At rest, the velocity of the ball is zero. Therefore, the momentum also becomes zero (product of mass and velocity). When the player kicks, the velocity increases, and the momentum also increases. This instant change or fluctuation of momentum results in impulse. This impulse is now responsible for the travel of the football over a long distance. To understand the impulse in detail, let’s firstly understand momentum.

Momentum 

Momentum is a very common word we often hear (especially in sports). In physics, it has quite broad significance. It is the measurement of mass in motion. This states that the higher the amount of momentum of an object, the greater will be the force required to stop the object. When this force acts on the object, the velocity and momentum both are affected. It is a vector quantity with the unit as kg. m/s.

p represents the momentum. So, according to the definition, the formula of momentum shall be:

p= m.v

m= mass of the object

v= velocity

According to the kinematic equation, Δv (velocity) is often written as aΔt. So, the equation shall be as follows:

p= mΔv

p=m.a.Δt [F=ma]

p=FΔt

Impulse 

It has a representative symbol, i.e. J. Thus, the impulse equation is as follows:

J= F. Δt

Thus, calculation of it involves the product of force with net time. The impulse concept gives us a better understanding of the conservation of momentum. As the forces continuously vary, thus, impulse becomes a significant part of physics. 

Impulse Momentum Theorem

According to the Impulse momentum theorem, the body experiencing a certain impulse will always be equal to its change of momentum. 

ΔtF=m(vf) –m (vi)

m(vi)= initial momentum

m(vf)= final momentum

Assume there is no change in the mass of the initial and final momentum, and then the equation shall be as:

ΔtF=m (vf – vi)

The theorem verifies or tells that the amount of force with a small velocity but for a long time will produce the same change in velocity velocity as a greater force but for a shorter time. 

Specific Impulse

It is the attribute for those engines that can produce a thrust force. For example, Rockets and Jet Engines. Thus, we can say that a specific impulse is the efficiency of an engine that uses fuel to produce thrust. 

Isp= F.tmfuel.g

Unit of specific impulse= seconds (other units cancels out)

Q- Find the impulse of the ball when a batsman hits it at an angle of 60 degrees. There is no change in the initial speed, i.e. 108 km/h. The ball strike by the batsman possesses a mass of 100g.

Solution:

As we have discussed, 

Impulse and change of momentum are both equal.

Thus, the initial momentum (before hitting the ball) = mass.velocity

= 0.1× 108 

= 10.8× 1000 m/km× (1hr/60s)

=180 kg m/s

Now, momentum after the batsman hits the ball,

= -180× cosine (60°)

=-180× 0.5

=-90 kg m/s

Impulse (change in momentum) = 180- (-90)

=270 m/s

Conclusion

Impulse is the amount or quantity of force acting on a certain body in a given time that changes its momentum. The amount of effect a force brings is directly proportional to the amount of time the force acts. Force and impulse both are vectors (quantity with both magnitude and direction) quantity. According to momentum in physics, it is the measure of mass in motion. This states that the higher the amount of momentum of an object, the greater will be the force required to stop the object. Impulse and momentum are interlinked. Moreover, According to the Impulse momentum theorem, the body experiencing a certain impulse will always be equal to its change of momentum.