Momentum

Momentum is a fundamental concept in mechanics that describes how objects move and interact, particularly during collisions and force-related events. It helps explain why some objects are harder to stop than others and how forces affect motion. Understanding momentum is essential in various real-world applications, including car safety, sports, engineering, and rocket propulsion.

Definition of momentum

Momentum is a measure of an object's motion, which depends on both its mass and velocity. The greater the mass or velocity of an object, the greater its momentum.

Momentum Equation:

where:

• p = momentum (kg.m/s)

• m = mass (kg)

• v = velocity (m/s)

Example Calculation:

A car with a mass of 1000 kg is moving at a speed of 20 m/s. The momentum is calculated as:

p = 1000 × 20 = 20,000 kg.m/s

A heavier or faster object has greater momentum, making it more difficult to stop or change direction.

Definition of impulse

Impulse is the change in momentum caused by a force acting over a period of time. When a force is applied to an object, it changes its velocity, which results in a change in momentum.

Impulse Equation:

where:

• F = force (N)

• Δt = time (s)

• Δ(mv) = change in momentum (Ns)

Example Calculation:

A force of 10 N acts on a 2 kg object for 3 seconds. What is the change in momentum?

Impulse = 10 × 3 = 30 Ns

Impulse is equal to the change in momentum. This explains why airbags and padded surfaces reduce injuries by increasing the time of impact, thereby reducing the force experienced by a person.

Conservation of momentum

The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. This means that momentum before a collision or explosion is equal to the total momentum after.

Example: Collision Between Two Cars

A 1000 kg car is moving at 10 m/s when it collides with a stationary 2000 kg car. After the collision, they move together at a final speed v.

(1000 × 10) + (2000 × 0) = (1000 + 2000) × v

10,000 = 3000v

v = 10,000 / 3000 = 3.33 m/s

Momentum is always conserved in a closed system, meaning the total momentum before and after the collision remains the same.

Resultant force and change in momentum

Newton’s Second Law of Motion states that the force acting on an object is equal to the rate of change of its momentum.

where:

• F = force (N)

• Δp = change in momentum (kg m/s)

• Δt = time (s)

Example: A Moving Ball

A 5 kg ball is moving at 6 m/s. If the ball is stopped in 0.5 seconds, what force is needed?

Δp = 5(6−0) = 30 kg.m/s

F = 30/0.5 = 60 N

If the stopping time increases, the force needed decreases. This is why airbags, crumple zones in cars, and padded sports gear help reduce injuries by extending the impact time.

Applications of momentum and impulse