Momentum in Collisions and Explosions

This lesson covers momentum, the conservation of momentum, and how these concepts apply to collisions and explosions — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You also need to understand how momentum concepts relate to vehicle safety features.

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What Is Momentum?

Momentum is a measure of how much motion an object has. It depends on both the mass and velocity of the object.

Momentum = Mass × Velocity

p = m × v

Quantity	Symbol	Unit
Momentum	p	Kilogram metres per second (kg m/s)
Mass	m	Kilograms (kg)
Velocity	v	Metres per second (m/s)

Key Points

• Momentum is a vector quantity — it has both magnitude and direction.
• The direction of the momentum is the same as the direction of the velocity.
• A stationary object has zero momentum (v = 0).
• A heavier object moving at the same speed has more momentum.
• A faster object of the same mass has more momentum.

Worked Example 1

A car of mass 1500 kg travels at 20 m/s. What is its momentum?

p = mv = 1500 × 20 = 30,000 kg m/s

Worked Example 2

A tennis ball (mass 0.058 kg) is served at 50 m/s. What is its momentum?

p = mv = 0.058 × 50 = 2.9 kg m/s

Exam Tip: Always include the direction when stating momentum (e.g. "30,000 kg m/s to the right"). Since momentum is a vector, direction matters — especially in collision and explosion calculations.

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Conservation of Momentum

In a closed system (where no external forces act), the total momentum before an event is equal to the total momentum after the event.

Total momentum before = Total momentum after

This is known as the law of conservation of momentum.

Important Conditions

• The system must be closed — no external resultant force acts on it.
• Momentum is conserved in all collisions and explosions (as long as the system is closed).
• This applies even when kinetic energy is not conserved (inelastic collisions).

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Types of Collision

Elastic Collisions

• Both momentum AND kinetic energy are conserved.
• Objects bounce off each other.
• Perfectly elastic collisions are rare in everyday life — but nearly elastic examples include collisions between snooker balls or gas molecules.

Inelastic Collisions

• Momentum is conserved but kinetic energy is NOT conserved.
• Some kinetic energy is converted to other forms — usually heat and sound.
• Most real-world collisions are inelastic.
• A perfectly inelastic collision is one where the objects stick together after the collision.

Feature	Elastic Collision	Inelastic Collision
Momentum conserved?	Yes	Yes
Kinetic energy conserved?	Yes	No (some KE converted to heat/sound)
Objects after collision	Bounce apart	May stick together or deform
Example	Snooker balls	Car crash

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Worked Examples: Collisions

Worked Example 3: Two Objects Colliding and Sticking Together

A trolley of mass 2 kg moving at 3 m/s collides with a stationary trolley of mass 1 kg. They stick together. Find the velocity after the collision.

Total momentum before = (2 × 3) + (1 × 0) = 6 + 0 = 6 kg m/s

Total momentum after = (2 + 1) × v = 3v

By conservation: 3v = 6

v = 6 ÷ 3 = 2 m/s

Worked Example 4: Two Objects Colliding and Bouncing Apart

A 3 kg ball moving at 4 m/s to the right collides head-on with a 2 kg ball moving at 1 m/s to the left. After the collision, the 3 kg ball moves at 1 m/s to the right. Find the velocity of the 2 kg ball after the collision.

Take rightward as positive:

Momentum before = (3 × 4) + (2 × (−1)) = 12 − 2 = 10 kg m/s

Momentum after = (3 × 1) + (2 × v) = 3 + 2v

By conservation: 3 + 2v = 10

2v = 7

v = 3.5 m/s (to the right)

Exam Tip: Always define a positive direction before starting a momentum calculation. Objects moving in the opposite direction should be given a negative velocity. This avoids sign errors, which are very common.

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Explosions

An explosion is when objects that are initially together move apart. Examples include a gun firing a bullet, a person jumping off a boat, or two ice skaters pushing apart.

Key Principle

Before the explosion, the total momentum is usually zero (everything is stationary).

By conservation of momentum, the total momentum after must also be zero.

This means the momenta of the objects after the explosion must be equal in magnitude and opposite in direction.

Worked Example 5: Gun and Bullet

A gun of mass 4 kg fires a bullet of mass 0.05 kg at 300 m/s. Find the recoil velocity of the gun.

Total momentum before = 0 (both at rest)

Total momentum after = (0.05 × 300) + (4 × v) = 0

15 + 4v = 0

4v = −15

v = −3.75 m/s

The gun recoils at 3.75 m/s in the opposite direction to the bullet.

Worked Example 6: Ice Skaters Pushing Apart

Skater A (mass 60 kg) and Skater B (mass 80 kg) are standing still on ice. They push apart. Skater A moves at 2 m/s to the left. Find Skater B's velocity.

Total momentum before = 0

After: (60 × (−2)) + (80 × v) = 0

−120 + 80v = 0

80v = 120

v = 1.5 m/s (to the right)

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Force, Momentum and Time

Newton's Second Law can also be expressed in terms of momentum:

Force = Rate of Change of Momentum

F = Δp / Δt

Where:

• F = resultant force (N)
• Δp = change in momentum (kg m/s)
• Δt = time taken for the change (s)

This equation shows that the same change in momentum can be achieved by:

• A large force over a short time, OR
• A small force over a long time

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Safety Applications

Vehicle safety features are designed to increase the time over which momentum changes during a collision, thereby reducing the force on the occupants.