Linear Momentum

Momentum:

Momentum of a body is the product of the mass of a body and its linear velocity. The symbol that is used to represent momentum is p.

Momentum, p = mass (m) × velocity (v)

p = kg × ms^-1.

Its unit is kgms^-1. It is a vector quantityVector quantities are quantities with magnitude and direction. Examples of vector quantities include displacement, velocity, position, force, and torque. More.

The momentum of a body depends on the mass and the velocity with which the body is moving. Its direction is the same as the direction of the object’s velocity.

A bus can have a large momentum even if it’s moving slowly because of its large mass.

A bullet can have a large momentum even though it has a small mass because it’s moving with a high velocity.

If an object is at rest it has no momentum no matterScience meaning: Matter is any substance (often a particle) that has mass, and also volume (occupies space). Matter exists in three states, solid, liquid and gas and is made up of... More how large its mass is.

In this case mass × 0 velocity = 0 Momentum

Example 1:

A car of mass 145 g moves with a velocity of 30m/s. Calculate the momentum of the car.

Solution:

Values given:

Mass = 145 g =  \( \frac{145}{1000} \) = 0.145 kg
velocity = 30 m/s
momentum = ?

Momentum, p = m × v

p = 0.145 x 30 = 4.35 Nm

Momentum = 4.35 kgm/s

Example 2:

Given that the momentum of a train is 354 kgm/s, calculate the mass if its velocity is 17.6 m/s.

Soultion:

Values given:

Momentum = 354 kgm/s
velocity = 17.6 m/s
mass = ?

Momentum, p = mass × velocity

make mass the subject of the formula

mass = \( \frac{momentum}{velocity} \)

mass = \( \frac{354}{17.6} \)

mass = 20.11kg

Example 3:

A train of mass 6000kg moves with a velocity V. If the momentum of the train is 1000Nm, calculate the velocity of the train.

Solution:

Values given:

Momentum = 1000 Nm
velocity = ?
mass = 6000kg

Momentum, p = mass × velocity

make velocity the subject of the formula

velocity = \( \frac{momentum}{mass} \)

Substitute the values

velocity = \( \frac{1000}{6000} \)

velocity = 0.167 m/s

Example 4:

A body of mass 20kg moves with a velocity of 10ms^-1, calculate its linear momentum

Solution:

Values given:

mass = 20kg
velocity = 10ms^-1

Momentum = mass × velocity

= 20kg × 10ms^-1

Momentum = 200kgms^-1.

Impulse:

The impulse of a force is the product of average force and the time during which it acts on the body. A force which acts for a very short time is called impulsive force or simply impulse. Impulse is usually associated with collision and is also called a blow

Impulse = Force × time

I = F × t

Impulse = Newton × seconds

I = Ns

The unit of impulse is Ns. It is a vector quantity.

Example 5:

A force of 40N acts on a body for 5 seconds. What is the impulse experienced?

Solution:

Values given:

F = 40N, t = 5 secs.

Impulse = Force × time

Impulse = 40 × 5

 Impulse = 200Ns.

Example 6:

If a force of 45 N acts on 10.75 kg mass and the impulse is 44.94Ns, calculate the time for which the force acts on the object.

Solution:

Values given:

Force = 45N
mass = 10.75kg
Impulse = 44.94Ns

Impulse = Force × time

make time the subject of the formula

time = \( \frac{Impulse}{Force} \)

time = \( \frac{44.94}{45} \)

time = \( \frac{44.94}{45} \)

time = 0.998 = 1s

Example 7:

The impulse of a force is 458 Ns. If the force acts for 1465 seconds, calculate the magnitude of the force.

Solution:

Values given:

Force = ?, t = 1465 seconds, Impulse = 458 Ns

Impulse  = Force × time

make Force the subject of the formula

Force = \( \frac{Impulse}{time} \)

Force = \( \frac{458}{1465} \)

Force = 0.312N