P10.4 Momentum

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: (Higher tier) Momentum p = m v, closed systems and conservation of momentum in collisions and explosions. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• (Higher tier) calculate momentum using p = m v and give its unit
• (Higher tier) explain why momentum is a vector and use + and − signs for direction
• (Higher tier) state the law of conservation of momentum for a closed system
• (Higher tier) use conservation of momentum to analyse collisions and explosions

Key words

• Momentum: Mass × velocity, p = m v, in kg m/s.
• Vector: A quantity with both size and direction, such as velocity, force and momentum.
• Closed system: A group of objects on which no external forces act.
• Conservation of momentum: In a closed system, the total momentum before an event equals the total momentum after it.
• Collision: An event in which moving objects hit each other and exert forces on each other for a short time.
• Explosion: An event in which objects at rest are pushed apart, for example by a spring or by expanding gases.

What is momentum? (Higher tier)

Every moving object has momentum. A heavy, fast object – a loaded lorry on a motorway – has a lot of momentum and is very hard to stop.

momentum = mass × velocity p = m v

p = momentum in kilogram metres per second, kg m/s; m = mass in kg; v = velocity in m/s

Rearranged: v = p ÷ m and m = p ÷ v

Worked example: a cricket ball and a motorbike

Cricket ball: p = 0.16 kg × 35 m/s = 5.6 kg m/s
Motorbike and rider: p = 250 kg × 24 m/s = 6000 kg m/s

Answer: 5.6 kg m/s and 6000 kg m/s

Worked example: finding velocity

A football of mass 0.43 kg has 8.6 kg m/s of momentum. Calculate its velocity.
v = p ÷ m = 8.6 ÷ 0.43

Answer: v = 20 m/s

Momentum has direction

Velocity is a vector, so momentum is a vector too. Choose one direction as positive. Momentum in the opposite direction is then negative.

Left trolley: p = 1.5 × (+4.0) = +6.0 kg m/s. Right trolley: p = 2.0 × (−3.0) = −6.0 kg m/s. Total momentum = +6.0 + (−6.0) = 0, even though both trolleys are moving. If they collide and stop, the total momentum is still zero.

Exam tip: Always draw an arrow showing which direction you have chosen as positive, then put a sign on every velocity.

Conservation of momentum in collisions

In a closed system, the total momentum before an event is equal to the total momentum after the event.

A closed system is one with no external forces acting on it (or where they are too small to matter), such as trolleys on a low-friction runway or pucks on ice. The objects push on each other, but these internal forces are equal and opposite, so the total momentum does not change.

Worked example: checking the trolley results

momentum before = 0.60 × 0.80 + 0.20 × 0 = 0.48 kg m/s
momentum after = (0.60 + 0.20) × 0.60 = 0.48 kg m/s

Answer: the total momentum is unchanged, so momentum is conserved

Worked example: two skaters, both moving

A 60 kg skater moving at 4.0 m/s catches up with a 40 kg skater moving at 1.5 m/s in the same direction. They hold on to each other.
total momentum before = 60 × 4.0 + 40 × 1.5 = 240 + 60 = 300 kg m/s
after: (60 + 40) × v = 300, so v = 300 ÷ 100

Answer: v = 3.0 m/s in the original direction

Explosions

In an explosion, objects that start at rest are pushed apart. The total momentum before is zero, so the total momentum after must also be zero. The objects move off with equal and opposite momentum.

Worked example: two trolleys pushed apart

A 0.50 kg trolley and a 1.5 kg trolley are pushed apart from rest. The 0.50 kg trolley moves left at 0.90 m/s. Find the velocity of the 1.5 kg trolley.
total momentum after = 0: 0.50 × (−0.90) + 1.5 × v = 0
1.5 v = 0.45, so v = +0.30 m/s

Answer: 0.30 m/s to the right

The same idea explains why a rifle recoils when it is fired, why a skateboard shoots backwards when you jump off it forwards, and why two ice skaters who push apart move in opposite directions. The lighter object always moves faster.

Common mistakes

• Adding the sizes of momenta in opposite directions. After an explosion from rest the total momentum is zero, not double.
• Giving the unit of momentum as N or kg/m s. It is kg m/s.
• Forgetting to add the two masses when objects stick together after a collision.
• Mixing up momentum (m v, a vector) with kinetic energy (½ m v², a scalar).
• Using conservation of momentum when large external forces act, such as friction from a rough surface.

Revision questions

Try these, then check your answers below each one.

Question 1. (Higher tier) Calculate the momentum of a 0.17 kg ice hockey puck moving at 25 m/s.

Answer: 4.25 kg m/s

Working: p = 0.17 × 25 = 4.25 kg m/s.

Question 2. (Higher tier) What is the unit of momentum? (Choose from: kg m/s, N, kg/m s, J.)

Answer: kg m/s

Working: Momentum = mass (kg) × velocity (m/s), so its unit is kg m/s.

Question 3. (Higher tier) An 800 kg car has a momentum of 17 600 kg m/s. Calculate its velocity.

Answer: 22 m/s

Working: v = 17 600 ÷ 800 = 22 m/s.

Related lessons

• Previous lesson: P10.3 Forces and Braking
• Next lesson: P10.5 Forces and Elasticity
• In this chapter: P10.1 Forces and Acceleration
• In this chapter: P10.2 Weight and Terminal Velocity
• In this chapter: P10 RP Required Practicals: Force, Extension and Acceleration

Continue in the full course

This lesson is section P10.4 (AGCSC3904) of our free GCSE Combined Science course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Combined Science course.