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10.4 Momentum

GCSE Physics · AQA · Chapter 10: Force and Motion

A free GCSE Physics lesson for AQA (8463) 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 in which objects stick together
  • (Higher tier) explain why objects pushed apart from rest move off with equal and opposite momentum

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 resultant force acts.
  • 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.
  • Recoil: The backward movement of one object when another is pushed or fired forwards from it.

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 hockey ball and a car

Hockey ball: p = 0.16 kg × 25 m/s = 4.0 kg m/s
Car: p = 1500 kg × 12 m/s = 18 000 kg m/s

Answer: 4.0 kg m/s and 18 000 kg m/s

Worked example: finding velocity

A tennis ball of mass 0.058 kg has 2.9 kg m/s of momentum. Calculate its velocity.
v = p ÷ m = 2.9 ÷ 0.058

Answer: v = 50 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 = 2.0 × (+3.0) = +6.0 kg m/s. Right trolley: p = 3.0 × (−2.0) = −6.0 kg m/s. Total momentum = +6.0 + (−6.0) = 0, even though both trolleys are moving.

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 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. The objects push on each other, but these internal forces are equal and opposite, so the total momentum does not change.

Testing it with trolleys. Trolley A is pushed into a stationary trolley B. A pin and cork make them stick together. A motion sensor (or light gates and a data logger) measures the velocity of A before and of both trolleys after.

Worked example: checking the trolley results

momentum before = 0.80 × 0.60 + 0.40 × 0 = 0.48 kg m/s
momentum after = (0.80 + 0.40) × 0.40 = 0.48 kg m/s

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

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 1.0 kg trolley and a 2.0 kg trolley are pushed apart from rest. The 1.0 kg trolley moves left at 0.50 m/s. Find the velocity of the 2.0 kg trolley.
total momentum after = 0: 1.0 × (−0.50) + 2.0 × v = 0
2.0 v = 0.50, so v = +0.25 m/s

Answer: 0.25 m/s to the right

The same idea explains 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 skater always moves faster.

Key fact: If two trolleys pushed apart reach blocks at the same moment, the ratio of the distances travelled equals the ratio of their speeds. A trolley of twice the mass travels half as far.

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 0.16 kg hockey ball moving at 30 m/s.

Answer: 4.8 kg m/s

Working: p = m v = 0.16 kg × 30 m/s = 4.8 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: p = m v, so the unit is kg × m/s = kg m/s.

Question 3. (Higher tier) A 1200 kg car has a momentum of 21 600 kg m/s. Calculate its velocity.

Answer: 18 m/s

Working: v = p ÷ m = 21 600 ÷ 1200 = 18 m/s.

Related lessons

Continue in the full course

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