How to calculate the change in momentum of an object?

The momentum of an object is a vector quantity equal to the product of its velocity and mass. A body can only develop momentum when an external force acts on it. When a net force is applied to an object, it alters its momentum during the application of the force. In other words, the rate at which momentum changes is determined by the short-term force supplied to the body. If an object experiences a substantial momentum shift in a short period of time, a large net force must have been applied to it. This forms the basis for the concept of change in the momentum of a body.

How to calculate the change in momentum of an object?

The change in the momentum is equal to the product of the mass and the change in the velocity. The mass remains the same as it is a constant value. It is the change in velocity which brings a change in momentum. 

The change in momentum is denoted by the symbol Δp. 

Its unit of measurement is the same as momentum, that is, kilograms meter per second (kg m/s), and the dimensional formula is given by [M¹L¹T^-1].

Δp =  m Δv

where,

• Δp is the change in momentum,
• m is the mass of object,
• Δv is the change in velocity of object.

According to Newton’s second law of motion, the force applied to the object is equal to the rate of change of momentum with respect to time. If the force remains constant across a given time period, the product of force and time change gives us the change in momentum.

Δp =  F Δt

where,

• Δp is the change in momentum,
• F is the force applied on the body,
• Δt is the time interval for which force acts on the object.

Sample Problems

Problem 1: Calculate the change in momentum of an object of mass 2 kg and change in velocity 20 m/s.

Solution:

We have,

m = 2

Δv = 20

Using the formula we get,

Δp =  m Δv

= 2 (20)

= 40 kg m/s

Problem 2: Calculate the change in momentum of an object of mass of 3 kg and change in velocity of 40 m/s.

Solution:

We have,

m = 3

Δv = 40

Using the formula we get,

Δp =  m Δv

= 3 (40)

= 120 kg m/s

Problem 3: Calculate the change in momentum of an object of mass 3 kg, initial velocity 30 m/s, and final velocity 60 m/s.

Solution:

We have,

m = 3

v_i = 30

v_f = 60

Calculate the change in velocity.

Δv = 60 – 30

= 30 m/s

Using the formula we get,

Δp =  m Δv

= 3 (30)

= 90 kg m/s

Problem 4: Calculate the change in momentum of an object of mass 4 kg, initial velocity 25 m/s, and final velocity 75 m/s.

Solution:

We have,

m = 3

v_i = 25

v_f = 75

Calculate the change in velocity.

Δv = 75 – 25

= 50 m/s

Using the formula we get,

Δp =  m Δv

= 4 (50)

= 200 kg m/s

Problem 5: Calculate the change in momentum of an object if a force of 12 N acts on it for 3 seconds.

Solution:

We have,

F = 12

Δt = 3

Using the formula we get,

Δp =  F Δt

= 12 (3)

= 36 kg m/s

Problem 6: Calculate the force that acts on a body for 6 seconds to produce a momentum change of 1200 kg/ms.

Solution:

We have,

Δp = 1200

Δt = 6

Using the formula we get,

Δp =  F Δt

F = Δp/Δt

= 1200/6

= 200 N

Problem 7: Calculate the time interval for which a force of 50 N acts on a body to produce a momentum change of 500 kg/ms.

Solution:

We have,

Δp = 500

F = 50

Using the formula we get,

Δp =  F Δt

Δt = Δp/F

= 500/50

= 10 s

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