The shape of the lesson
By the end of the lesson, learners can
- More force, more acceleration: A constant force pushes a cart on a frictionless track.
- The three laws: Linear momentum is p = mv, a vector pointing along the velocity, measured in kg m s⁻¹.
- Spotting a third-law pair.
- F = ma: F is the resultant force, a is in the same direction.
- Momentum: p = mv; force = rate of change of momentum.
- Third law: pair acts on two different bodies, same type of force.
One picture every idea returns to
Mass measures inertia, the resistance to a change in motion. Newton's first law: with no resultant force, velocity stays constant. Second law: the resultant force equals the rate of change of momentum, F = Δp / Δt, which for constant mass becomes F = ma. Third law: forces come in pairs that are equal, opposite, of the same type, and act on two different bodies. Weight is the pull of gravity, W = mg.
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, Force is what changes momentum.. Kinematics described motion; dynamics explains it. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: More force, more acceleration | A constant force pushes a cart on a frictionless track. Project tab 1 of the lab (Newton’s laws (F = ma)) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: The three laws | Linear momentum is p = mv, a vector pointing along the velocity, measured in kg m s⁻¹. | Pairs |
| 21 to 30 min | Teach and check: Spotting a third-law pair | Spotting a third-law pair. | Cooperative Concept Mapping |
| 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, 16 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 Spotting a third-law pair, 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.
Cooperative Concept Mapping
Teams receive the key terms on cards and arrange them on a large sheet, drawing and labelling the links. Compare maps between teams before showing the model map.
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 |
|---|---|
| The classic error is to pair the weight of an object with the normal contact force from the surface it rests on. | They act on the same body and can be different types and sizes (think of an object on a slope), so they are not a third-law pair. A true pair always acts on two different bodies and is the same type of force. Also keep mass and weight distinct: mass (kg) is the same everywhere, while weight (N) is mg and changes with g. |
Newton's laws and momentum: worksheet
6 questions, 16 marks. Written in the style of the papers; no past paper question is reproduced.
A constant resultant force of 18 N acts on a 4.0 kg object initially at rest. Find its acceleration and its velocity after 5.0 s.
A 0.058 kg tennis ball is served, leaving the racket at 50 m s⁻¹ from rest. The racket is in contact with the ball for 5.0 ms. Find the change in momentum and the average force on the ball.
A 1200 kg car is towed by a rope. The driving situation gives a forward pull of 3000 N while resistive forces total 1800 N. Find the acceleration of the car.
A swimmer pushes backward on the wall of a pool and moves forward. State the Newton's third law pair to "the swimmer pushes backward on the wall", and explain how this makes the swimmer move.
An astronaut has a mass of 80 kg. Taking g = 9.8 N kg⁻¹ on Earth and g = 1.6 N kg⁻¹ on the Moon, find the astronaut's weight in each place, and state the mass on the Moon.
A 0.50 kg ball moving at 4.0 m s⁻¹ is struck and moves off at 4.0 m s⁻¹ in the opposite direction. Find the magnitude of the change in momentum, and explain why it is not zero even though the speed is unchanged.
Answer key and marking notes
- a = F / m = 18 / 4.0 = 4.5 m s⁻². ✓
- v = u + at = 0 + 4.5 × 5.0 = 22.5 m s⁻¹. ✓
- Δp = mΔv = 0.058 × 50 = 2.9 kg m s⁻¹. ✓
- F = Δp / Δt = 2.9 / (5.0 × 10⁻³) = 580 N. ✓
- Resultant force = 3000 − 1800 = 1200 N. ✓
- a = F / m = 1200 / 1200 = 1.0 m s⁻². ✓
- The pair is "the wall pushes forward on the swimmer", equal in size and opposite in direction. ✓
- This forward force from the wall is the resultant push on the swimmer, so by F = ma the swimmer accelerates forward. ✓
- On Earth: W = mg = 80 × 9.8 = 784 N. ✓
- On the Moon: W = 80 × 1.6 = 128 N. ✓
- Mass is unchanged at 80 kg; only the weight differs because g differs. ✓
- Take the new direction as positive: Δp = m(v − u) = 0.50(4.0 − (−4.0)) = 0.50 × 8.0 = 4.0 kg m s⁻¹. ✓
- Momentum is a vector; the direction reversed, so even with equal speeds the momentum changed by 4.0 kg m s⁻¹. ✓
17 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.
Newton's first law states that an object continues at rest or at constant velocity unless:
- Aacted on by a resultant force
- Bit runs out of energy
- Ca force is removed
- Dits mass changes
A resultant force of 20 N acts on a 5.0 kg mass. Its acceleration is:
- A100 m s⁻²
- B0.25 m s⁻²
- C4.0 m s⁻²
- D15 m s⁻²
The property of a body that measures its resistance to a change in motion is its:
- Aweight
- Bmass
- Cmomentum
- Dspeed
A 0.20 kg ball moves at 15 m s⁻¹. Its momentum is:
- A75 kg m s⁻¹
- B0.013 kg m s⁻¹
- C30 kg m s⁻¹
- D3.0 kg m s⁻¹
The SI unit of linear momentum is:
- Akg m s⁻¹
- Bkg m s⁻²
- CN s⁻¹
- Dkg m² s⁻¹
One newton can be defined as the resultant force that gives a 1 kg mass an acceleration of:
- A9.8 m s⁻²
- B1 m s⁻¹
- C1 m s⁻²
- D1 kg m s⁻¹
On Earth where g = 9.8 N kg⁻¹, the weight of a 5.0 kg object is:
- A5.0 N
- B49 N
- C0.51 N
- D9.8 N
A Newton's third law pair of forces always:
- Aacts on the same body
- Bcan be different types of force
- Calways cancels out
- Dacts on two different bodies and is the same type
A rocket accelerates upward by ejecting exhaust gas downward. The upward push on the rocket is the third-law pair of:
- Athe downward push of the rocket on the gas
- Bthe weight of the rocket
- Cthe upward push of the rocket on itself
- Dair resistance
A 3.0 kg object is pulled by a 10 N force while a 4.0 N friction force opposes it. Its acceleration is:
- A4.7 m s⁻²
- B3.3 m s⁻²
- C2.0 m s⁻²
- D14 m s⁻²
If the resultant force on a moving object is zero, the object:
- Acomes to rest at once
- Bmoves at constant velocity
- Caccelerates uniformly
- Dmust be stationary
Impulse is defined as:
- Aforce divided by time
- Bmass times acceleration
- Cthe change in kinetic energy
- Dforce multiplied by the time for which it acts
A force acts on a body and its momentum changes by 12 kg m s⁻¹ in 3.0 s. The average force is:
- A4.0 N
- B36 N
- C9.0 N
- D0.25 N
An astronaut travels from Earth to the Moon. Which quantity stays the same?
- Athe weight
- Bthe gravitational field strength
- Cthe mass
- Dthe value of g
A 0.45 kg football is kicked from rest and leaves the foot at 24 m s⁻¹ after a contact time of 0.018 s. The average force is about:
- A11 N
- B600 N
- C430 N
- D1100 N
A person stands in a lift that accelerates upward. The normal contact force from the floor on the person is:
- Aequal to the person's weight
- Bless than the person's weight
- Czero
- Dgreater than the person's weight
A constant 6.0 N resultant force acts on a 2.0 kg trolley for 4.0 s from rest. Its final momentum is:
- A24 kg m s⁻¹
- B12 kg m s⁻¹
- C48 kg m s⁻¹
- D3.0 kg m s⁻¹
Quiz key
With no resultant force, velocity does not change. A force is needed to change the motion.
a = F / m = 20 / 5.0 = 4.0 m s⁻².
Mass is the measure of inertia. Weight is the gravitational force on the mass.
p = mv = 0.20 × 15 = 3.0 kg m s⁻¹.
Momentum = mass × velocity = kg × m s⁻¹ = kg m s⁻¹ (equivalently N s).
1 N = 1 kg × 1 m s⁻², so it gives a 1 kg mass an acceleration of 1 m s⁻².
W = mg = 5.0 × 9.8 = 49 N.
A third-law pair is equal and opposite, the same type, and acts on two different bodies.
The rocket pushes the gas down; by the third law the gas pushes the rocket up. The pair acts on the gas and the rocket.
Resultant = 10 − 4.0 = 6.0 N; a = 6.0 / 3.0 = 2.0 m s⁻².
Zero resultant force means zero acceleration, so the velocity is constant (which may be non-zero).
Impulse = F × t, and it equals the change in momentum, Δp.
F = Δp / Δt = 12 / 3.0 = 4.0 N.
Mass is the same everywhere. Weight, g and the field strength are all smaller on the Moon.
Δp = 0.45 × 24 = 10.8 kg m s⁻¹; F = 10.8 / 0.018 = 600 N.
To accelerate upward the resultant force is upward, so the upward contact force exceeds the downward weight.
Δp = Ft = 6.0 × 4.0 = 24 kg m s⁻¹, starting from zero, so the final momentum is 24 kg m s⁻¹.
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.