# Difference between Momentum and Impulse

Last Updated : 04 Feb, 2024

Mechanics is a branch of mathematics and physics that studies the interactions of force, matter, and motion among physical things. Displacements, or changes in an object’s location relative to its environment, are caused by forces applied to it.Â

Mechanics is a part of classical physics that deals with bodies that are either at rest or moving at speeds slower than the speed of light. It’s also known as the physical science that studies the motion of bodies and forces on them that aren’t in the quantum domain.

### What is Momentum?

Momentum is defined as the quantity of motion multiplied by the amount of matter moved and the speed at which it travels. When you walk, run, or do anything else, you’re creating momentum. If a bicycle and a car both ride at the same speed down the street, the automobile will have the most momentum. The SI unit of momentum is kg m/s.

The quantity of momentum is a vector quantity.

Formula for Momentum:

p = mÃ—v

where,

• p is the momentum,
• m is the mass of an object, and
• v is the velocity.

### What is Impulse?

The impulse is a term that refers to the product of the average net force acting on an object over a period of time. It is denoted by the letter J and is usually measured in Newton seconds or kilograms per second.

Formula for Impulse:

Â J = FÃ—Î”tÂ

where,

• J is the impulse.
• Î”t is the time interval, and
• F is the force.

### Difference between Momentum and ImpulseÂ

 Momentum Impulse Momentum can be defined as a measure of an object’s resistance to stopping. The terms “impulse” and “momentum” are interchangeable. The term “impulse” refers to a quantity that expresses the influence of a net force applied on an object. The symbol of momentum is p. The symbol of impulse is J. S.I unit of momentum is kg m/s or Kilogram meter per second. S.I unit of impulse is Newton-seconds (Ns) or kg m/s. The formula for momentum is:Â  p = mÃ—v The formula for impulse is: J = FÃ—Î”t The formula is used to calculate when force is required. The formula is used to calculate the force which acts. For example, if momentum, despite its little mass, a bullet has a considerable momentum due to its extraordinarily high velocity. Example of impulse, when a player hits the ball in baseball, it experiences a quick shift in momentum. As a result, there is a quick reaction time and a large impulsive force develops.

### Sample Problems

Problem 1: Calculate the impulse on a body struck by a 500 N force with a 0.1 s contact time. Â

Solution:

The force exerted on body is F = 100N

Time Î”t = 0.1s

Therefore, impulse is:

J = F Ã— Î”t

= (500) Ã— (0.1)Ns

= 50 Â Ns

Hence, the impulse is 50 Ns.

Problem 2: Calculate the momentum of a 10-kg object moving at a 5 m/s speed.

Solution:

Â Â

Given,

Mass of an object m is 10kg

Velocity v is 5m/s

Therefore, the momentum is:

p=mÃ—v

p = (10)Ã—(5)

= 50 kg.m/s

Problem 3: Calculate the momentum of a 500g ball thrown at 100 metres per second.

Solution:

Given,

Mass of an object m = 500gm

Velocity v is 100m/s

Therefore, the momentum is:

p = m Ã— v

= (500)Ã—(100)

= 5000 gm/s

Problem 4: Calculate the momentum of a 40-gram ball thrown at a speed of 10 metres per second.

Solution:

Given,

Mass of an object m = 40gm

Velocity Â v is 10m/s

Therefore, the momentum is:

p = m Ã— v

= (40)Ã—(10)

= 400 gm/s

Problem 5: Why does a person sustain more injuries when they fall onto a floor rather than sand?

Solution:

When someone falls from a bed to the floor, they suffer greater damage than if they fall into a sand pile. Because the sand yields more than the cemented floor, the contact time increases and the force impact decreases.

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