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Impulse Formula

Exam

Kitiyala Jamir

Updated on 02nd March, 2023 , 3 min read

What is Impulse?

An impulse is the sum of a force, F, over the period of time it acts, t. Since force is a vector quantity, impulse also belongs to this category. When an object receives an impulse, it experiences an equivalent vector change in its linear momentum and also in the direction that results.

SI unit: newton-second (N⋅s) (kg⋅m/s in SI base units)

Other units: pound⋅s

What is Momentum?

The sum of a particle's mass and velocity is known as momentum. Momentum has a magnitude and a direction because it is a vector quantity. The second law of motion of Isaac Newton states that the force acting on a particle is equal to the time rate of change of momentum. 

For example,

 If a football game ends in a tie, each team is given a certain number of penalty shots. As a result, when the player kicks the ball, which is at rest and has no momentum, to shoot for the goal, the momentum increases due to the development of velocity. This sudden change in momentum causes an impulsive force to be generated. The impulsive force assists the ball in traveling long distances in a short amount of time.

The impulse is a large force that acts for a very short period of time. It is represented by J

The Impulse Formula is expressed as

J=F×t

Where,

  • The applied force is denoted as F.
  • The time interval during which force is applied is denoted by the symbol t.

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

J=m×v

Where,

  • The body's mass is denoted as m.
  • The velocity with which the body moves is denoted by v.

Velocity is expressed as

v=vf – vi

Where,

  • The initial velocity is denoted by vi.
  • The final velocity is denoted as vf.

As a result, the Impulsive force is expressed as

f=mvf−vit

The impulsive force is articulated in Newton(N) and the impulsive force is articulated in Kgms-1. 

Equation of Impulse Momentum

The following equation can be used to calculate Impulse: 

J = m * Δv

To put it simply,

Impulse = mass (m) * (Velocity2-Velocity1)

  • There are two points in time where velocity1 and velocity2 represent different speeds of movement. This is referred to as velocity change.

We can calculate the unit of impulse using the above equation:

Mass = in kg

Velocity = in m/s

J   = kg . m/s or N.s 

Solved Examples

Q1.After a free fall from a height, a 5-gram ball lands on the ground. Gravitational acceleration, g = 10 ms-2. The ball has a velocity of 6 ms-1 before colliding, and it is reflected upright at 4 m/s after the collision. Determine the impulse. 

Ans:

 Mass of the ball (m) = 5 gm = 0.005 kg

Before collision, velocity of ball (vo) = -6 m/s

After collision, velocity of ball (vt) = 4 m/s

The plus and minus signs indicate that the direction before the collision is opposite the direction after the contact.

Since we need to find out Impulse (J), so the solution will be

Impulse (J) = Total change in momentum (Δp)

J = Δp = m * vt – m * vo

= m * (vt – vo)

J = (0.005)(4 – (-6)) = (0.005)(4 + 6) = (0.005)(10) = 0.05 N.s (Ans.)

Q2. A batter hits a straight ball at the bowler while maintaining its initial 12 m/s speed. If the ball's mass is 0.15kg, calculate the impulse transferred to it. 

Ans: Given vi (Initial Velocity) = 12 m/s

vf (Final Velocity) = -12m/s

m (mass) = 0.15kg

Impulse is articulated as J = m * vf – m * vi

= m (vf – vi)

= 0.15 Kg (-12 -12) m/s = -3.6N.s

So, impulse = -3.6N.s (Ans.)

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Frequently Asked Questions

What is impulse write its formula?

The product of the average net force acting on an object for a given duration is often defined as the impulse. The equation for impulse is given as; J = F⋅Δt. Impulse, like force, is a vector quantity with a directional component.

What is impulse in force?

An impulse is a specific amount of force applied for a specific amount of time to cause a change in momentum.

Is impulse and momentum the same?

Momentum is defined as the resistance of an object to stopping. The terms "impulse" and "momentum" are synonymous. The term "impulse" refers to a unit of measurement that expresses the effect of a net force applied to an object. The symbol of momentum is p.

What are some of the common applications of impulse and momentum?

Some common applications include hitting a ball, a car accident, Golf, karate and so on.

What are the different units of impulse?

The unit of impulse is kg meter per second (kgm/s) or Newton second (Ns).

Is impulse denoted I or J?

The impulse is usually represented by the variable J (not to be confused with the polar moment of inertia, which is also represented by J), and momentum is defined as a body’s mass multiplied by its velocity.

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