The shape of the lesson
By the end of the lesson, learners can
- Collide, and keep the total: Set the masses and velocities of two trolleys, then let them collide.
- Counting the total momentum.
- Momentum: p = mv in kg m/s; it is a vector.
- Conservation: total momentum before = total momentum after (closed system).
- Direction: pick a positive direction and sign every velocity before adding.
One picture every idea returns to
Momentum is mass times velocity: p = mv, measured in kg m/s. It is a vector, so direction matters. In a closed system with no external resultant force, the total momentum before an interaction equals the total momentum after it.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Mass in motion, and what it keeps.. A heavy lorry crawling and a light bullet flying can carry the same punch. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Collide, and keep the total | Set the masses and velocities of two trolleys, then let them collide. Project tab 1 of the lab (Momentum and conservation) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Counting the total momentum | Counting the total momentum. Model the worked example Worked example on the board, one line at a time. | Numbered Heads Together |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Counting the total momentum, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Numbered Heads Together
Teams of four number off. Put up a question, give the team time to make sure every member can answer, then call a number: that student answers for the team, so nobody can leave the thinking to someone else.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Because momentum is a vector, you must include direction. | A trolley moving left has a negative velocity if right is positive, so its momentum is negative. Adding momenta without checking their signs is the single most common error examiners see in Paper 4. |
Momentum and conservation: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
Define momentum, give the equation for it, and state its unit.
Calculate the momentum of a 1500 kg car travelling at 12 m/s.
State the principle of conservation of momentum and the condition under which it applies.
A 3.0 kg trolley moving at 4.0 m/s collides with a stationary 1.0 kg trolley. They stick together. Calculate their common velocity afterwards.
A 0.50 kg ball moving at 6.0 m/s to the right strikes a stationary 1.0 kg ball. After the collision the 0.50 kg ball rebounds at 2.0 m/s to the left. Calculate the velocity of the 1.0 kg ball, taking the right as positive.
A stationary firework explodes into two pieces that fly apart. Use the conservation of momentum to explain why the two pieces move in opposite directions.
Answer key and marking notes
- Momentum = mass × velocity; p = mv. ✓
- Unit: kg m/s (it is a vector). ✓
- p = mv = 1500 × 12
18000 kg m/s
- The total momentum before an interaction equals the total momentum after it. ✓
- This holds when no external resultant force acts (a closed system). ✓
- before: p = 3.0 × 4.0 = 12 kg m/s
after: 12 = (3.0 + 1.0) × v
v = 12 ÷ 4.0
v = 3.0 m/s
- before: p = 0.50 × 6.0 = 3.0 kg m/s
after: 3.0 = 0.50 × (−2.0) + 1.0 × v
3.0 = −1.0 + v → v = 4.0 m/s
v = 4.0 m/s to the right
the rebound makes the ball's velocity −2.0, not +2.0
- Before the explosion the total momentum is zero (it is at rest). ✓
- Momentum is conserved, so the total afterwards must also be zero. ✓
- The two momenta must therefore be equal in size and opposite in direction, so the pieces move opposite ways. ✓
3 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A 0.50 kg ball moves at 6.0 m/s. What is its momentum?
- A0.083 kg m/s
- B3.0 kg m/s
- C6.5 kg m/s
- D12 kg m/s
A 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley, and they move off together. What is their common velocity after the collision?
- A1.0 m/s
- B2.0 m/s
- C3.0 m/s
- D6.0 m/s
Two ice skaters are initially at rest and push apart. The 60 kg skater moves left at 1.0 m/s. Ignoring friction, what happens to the 40 kg skater?
- Amoves right at 1.5 m/s
- Bmoves right at 1.0 m/s
- Cmoves left at 1.5 m/s
- Dstays at rest
Quiz key
p = mv = 0.50 × 6.0 = 3.0 kg m/s. Option D divides velocity by mass; C adds the numbers; A inverts the calculation.
momentum before = 2.0 × 3.0 = 6.0 kg m/s. After the collision the combined mass is 3.0 kg, so v = 6.0 ÷ 3.0 = 2.0 m/s. Option C wrongly keeps the original speed; D forgets to divide by the total mass.
The 60 kg skater carries 60 × 1.0 = 60 kg m/s to the left, so the 40 kg skater must carry 60 kg m/s to the right: v = 60 ÷ 40 = 1.5 m/s. Option B wrongly assumes equal speeds, ignoring the mass difference.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.