Impulse Formula

Impulse is a concept of physics that involves the study of dynamics, especially momentum. It expresses the effect of forces on the objects of motion over some time. Well, here is a simple guide that can help the students understand the formula of impulse and its applications.

What is Impulse?

Impulse is conventionally defined as the change in momentum an object undergoes, due to a force applied for some duration. It is a quantity, essentially, measuring the effect of a force on the state of an object's motion.

Impulse Formula

The formula for impulse (J)

            J=F⋅Δt

where:

• J is the impulse,

• F is the average force applied,

• Δt is the time interval over which the force is applied.

Impulse can also be said as the rate of change of momentum.

              J=m×v

Where,

• The mass of the body is taken as m

• The velocity with which the body moves is given as v.

Velocity is given  as

             v=vf-vi

Where,

• Initial Velocity is defined as vi

• Final Velocity is defined as vf.

Hence, the Impulsive force is expressed as

Impulse is expressed in Kgms-1 and Impulsive force is expressed in Newton(N).

Formula for impulse-momentum

The formula of Impulse-momentum is obtained from the impulse-momentum theorem, which states that the alteration in momentum of an object is equal to an impulse applied to the object. The formula is expressed as:

Impulse-momentum formula: 

J=Δp

When the mass is constant: 

FΔt=mΔv

When the mass is varying:  

Fdt=mdv+vdm

Since the SI unit of impulse and momentum are the same, thus it is expressed as Ns=kg.m.s-1

Solved Problems:

Following are some questions on impulse:

Problem 1: A batsman sends the ball straight back in the direction from where it was sent from without changing the initial speed of 12 m/sec. If the ball has a mass of 0.15kg. Find the impulsive delivered to the ball? 

Solutions:

Given:

vi (Initial Velocity) = 12 m/s,

vf(Final Velocity) = -12m/s,

m (mass) = 0.15kg,

J (Impulse) =?

Impulse is expressed as

Problem 2: A golfer hits a ball of mass 45g at a speed of 40m/s. The golf club is in contact for 3 s with the ball. Find out the average force applied by the club on the ball.

Answer:

m (Mass)= 0.045 kg,

vi (Initial Velocity) = 0,

vf (Final Velocity) = 40m/s,

Impulse force F = ma =