Course: Combined Science + Separate Physics | Tier: Higher only | Equation sheet: given in the exam
The equation
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) |
Rearranged: v = p ÷ m | m = p ÷ v | In a collision or explosion, total momentum before = total momentum after
Use FIFA for every answer
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Higher tier only: work through all 10. Most questions need rearranging.
Questions
Q1 A 0.16 kg cricket ball is bowled at 30 m/s. Calculate its momentum.
Show solution
F: p = m v
I: p = 0.16 × 30
F: p is already the subject
A: 4.8 kg m/s
Q2 A 1200 kg car has a momentum of 18 000 kg m/s. Calculate its velocity.
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F: p = m v
I: 18 000 = 1200 × v
F: v = 18 000 ÷ 1200
A: 15 m/s
Q3 A bowling ball rolls at 8 m/s with a momentum of 56 kg m/s. Calculate its mass.
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F: p = m v
I: 56 = m × 8
F: m = 56 ÷ 8
A: 7 kg
Q4 A 45 g golf ball has a momentum of 3.15 kg m/s just after being hit. Calculate its speed.
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Convert first: 45 g = 0.045 kg
F: p = m v
I: 3.15 = 0.045 × v
F: v = 3.15 ÷ 0.045
A: 70 m/s
Q5 A 1500 kg car has a momentum of 30 000 kg m/s. Calculate its speed in km/h.
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F: p = m v
I: 30 000 = 1500 × v
F: v = 30 000 ÷ 1500 = 20 m/s
A: 20 × 3600 ÷ 1000 = 72 km/h
Q6 A 1000 kg car moving at 12 m/s crashes into a stationary 1500 kg car. They lock together. Calculate their speed just after the crash.
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Momentum before: p = 1000 × 12 + 0 = 12 000 kg m/s
F: p = m v (after, combined mass 2500 kg)
I: 12 000 = 2500 × v
F: v = 12 000 ÷ 2500
A: 4.8 m/s
Q7 Two ice skaters stand still, then push apart. The 40 kg skater moves off at 3 m/s. Calculate the velocity of the 60 kg skater.
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Total momentum before = 0, so the two momenta after are equal and opposite
40 kg skater: p = 40 × 3 = 120 kg m/s
F: p = m v
I: 120 = 60 × v
F: v = 120 ÷ 60
A: 2 m/s in the opposite direction
Q8 A cruise ship with a mass of 1.0 × 108 kg has a momentum of 5.0 × 108 kg m/s. Calculate its speed.
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F: p = m v
I: 5.0 × 108 = 1.0 × 108 × v
F: v = 5.0 × 108 ÷ 1.0 × 108
A: 5.0 m/s
Q9 A 30 000 kg railway wagon moving at 2.0 m/s hits a stationary wagon and they couple together, moving off at 1.2 m/s. Calculate the mass of the second wagon.
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Momentum before: 30 000 × 2.0 = 60 000 kg m/s
F: p = m v (after)
I: 60 000 = m × 1.2
F: m = 60 000 ÷ 1.2 = 50 000 kg (both wagons)
A: second wagon = 50 000 − 30 000 = 20 000 kg
Q10 A 58 g tennis ball arrives at a racket at 25 m/s and leaves in the opposite direction at 35 m/s. Calculate the size of its change in momentum, to 2 significant figures.
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Convert first: 58 g = 0.058 kg; take the new direction as positive: before −25 m/s, after +35 m/s
F: p = m v
I: before = 0.058 × −25 = −1.45; after = 0.058 × 35 = 2.03
F: change = 2.03 − (−1.45) = 3.48 kg m/s
A: 3.5 kg m/s (2 s.f.)
Watch out: a change of direction means you add the speeds, not subtract.
