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# How hard do you need to push?

Year 10 Physics · Newton's laws

<!-- Speaker note: Students apply F = ma to find force, mass or acceleration with units, use the net force, and explain how changing force or mass changes acceleration (AC9S10U05, node 4, a hinge node). About 30 minutes (Engage and Explore 8 min · Explain 9 min · Practise 4 min · Evaluate 3 min · Typical adds 4 min, Wider about 2 min). -->

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## Today

**We are learning to** newton's second law: the net force on an object equals its mass times its acceleration, F = ma. Double the net force and the acceleration doubles; double the mass and the acceleration halves.

- I can use F = ma to find force, mass or acceleration, with correct units.
- I can explain that F in F = ma is the net force.
- I can explain what doubling the force or the mass does to the acceleration.

<!-- Speaker note: Before class: A concept tutorial for introducing or revising the idea; it does not replace a trolley and hanging-mass practical. Set the width with `?width=minimum`, `typical` (default) or `wider`. The hinge risks are using the applied force instead of the net force, and dropping units or direction. The net-force question in Explain targets the first. Board notes: the acceleration reading (under the board) is the net force divided by the mass, and shows before Play, so students can tune the push without running it. No friction on this board. Teacher: In your own words: the doubling paragraph is the evidence of the qualitative relationship. -->

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## Why it matters

> Push an empty shopping trolley and it shoots off. Push a full one just as hard and it barely gets going. Same push, different result: by exactly how much?

<!-- Speaker note: You know a net force makes things accelerate. This lesson finds the exact rule. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Engage: predict

**A push gives an empty trolley an acceleration of 4 m/s². You load it until its mass is doubled and push exactly as hard. Predict its acceleration.**

- 4 m/s²: the push is the same
- 8 m/s²
- A little less, maybe 3.5 m/s²
- 2 m/s²: half as much

<!-- Speaker note: What happens: 2 m/s². Doubling the mass halves the acceleration for the same net force: a = F ÷ m. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: put the four predictions on the board; come back after Explore. -->

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## Explore it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fscience%2Fphysics-10%2Ff-ma%2Fstep-2&code=widget%3A+forces%0Aobject%3A+Trolley%0Amass%3A+1%2C+10%2C+4%0Aforce+P%3A+right%2C+4%2C+Push%2C+adjust+0-40%0Amotion%3A+on%0Atrack%3A+80%0Atime%3A+6%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/science/physics-10/f-ma/?full=step-2#step-2)

<!-- Speaker note:  -->

<!-- Speaker note: Teacher: ask what push hit target 1 (8 N) and target 2 (16 N). Write F, m, a in a table. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* 2 m/s². Doubling the mass halves the acceleration for the same net force: a = F ÷ m.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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## The rule

**For 4 kg you needed 8 N; for 8 kg, 16 N. What rule links force, mass and acceleration?**

- Force = mass + acceleration
- Force = mass ÷ acceleration
- Force = mass × acceleration (F = ma)

* Answer: Force = mass × acceleration (F = ma)

<!-- Speaker note: 8 = 4 × 2 and 16 = 8 × 2. F is the net force in N, m the mass in kg, a the acceleration in m/s². -->

<!-- Speaker note: Teacher: students should say the rearrangement aloud for each number check. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the force

**What net force gives a 1200 kg car an acceleration of 3 m/s², in N?**

* Answer: 3600

<!-- Speaker note: F = ma = 1200 × 3 = 3600 N. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the acceleration

**A net force of 50 N acts on a 10 kg box. Its acceleration, in m/s²?**

* Answer: 5

<!-- Speaker note: a = F ÷ m = 50 ÷ 10 = 5 m/s². -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mass

**A net force of 600 N gives a sprinter an acceleration of 10 m/s². Her mass, in kg?**

* Answer: 60

<!-- Speaker note: m = F ÷ a = 600 ÷ 10 = 60 kg. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Net force

**A 2 kg box is pushed with 10 N against 4 N of friction. What force goes into F = ma?**

- The friction, 4 N
- The net force, 6 N
- The push, 10 N
- 14 N

* Answer: The net force, 6 N

<!-- Speaker note: Net force 10 − 4 = 6 N, so a = 6 ÷ 2 = 3 m/s². -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Units

**Match each quantity to its unit.**

| | |
|---|---|
| `Force (F)` | A. newtons (N) |
| `Mass (m)` | B. metres per second (m/s) |
| `Acceleration (a)` | C. kilograms (kg) |
| `Velocity (v)` | D. metres per second squared (m/s²) |

* Answer: Force (F) → A. newtons (N); Mass (m) → C. kilograms (kg); Acceleration (a) → D. metres per second squared (m/s²); Velocity (v) → B. metres per second (m/s)

<!-- Speaker note: F = ma only works with these units: mass in kg (not g), acceleration in m/s² (not m/s). -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Double, half or same

**What happens to the acceleration?**

Groups: Doubles · Halves · Stays the same

The net force doubles, same mass · The mass doubles, same net force · Both force and mass double · The net force halves, same mass

* Answer: The net force doubles, same mass → Doubles; The mass doubles, same net force → Halves; Both force and mass double → Stays the same; The net force halves, same mass → Halves

<!-- Speaker note:  -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Triple the force

**A trolley accelerates at 6 m/s². The net force is tripled and the mass stays the same. New acceleration, in m/s²?**

* Answer: 18

<!-- Speaker note: Three times the force, three times the acceleration: 18 m/s². -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Deceleration

**A 1500 kg car brakes from 20 m/s to rest in 4 s. What is the size of its deceleration, in m/s²?**

* Answer: 5

<!-- Speaker note: Δv ÷ Δt = 20 ÷ 4 = 5 m/s² (backwards). -->

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## Braking force

**What braking force does that need, in N?**

* Answer: 7500

<!-- Speaker note: F = ma = 1500 × 5 = 7500 N, backwards. -->

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## A loaded car

**The same car is loaded with people and luggage (more mass). To stop in the same time, the braking force must be…**

- the same
- smaller
- bigger

* Answer: bigger

<!-- Speaker note: F = ma: the same deceleration with more mass needs more force. With the same braking force, the loaded car would decelerate less and take longer to stop. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Elaborate: is it really a straight line?

**You measure a trolley's acceleration for several pulling forces, keeping the mass the same. What graph of acceleration against force does F = ma predict?**

- A curve that levels off
- A straight line through the origin (gradient 1 ÷ mass)
- A horizontal line

* Answer: A straight line through the origin (gradient 1 ÷ mass)

<!-- Speaker note: a = F ÷ m, so a is proportional to F: a straight line through the origin with gradient 1/m. Real data that misses the origin usually points to friction. What this step is for: Predicting the shape of an F–a graph before seeing data prepares students to assess linearity in a trolley practical. -->

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## Evaluate: look back

Write one sentence: "At first I thought… Now I think… because…"

**Revision summary**

- **Newton's second law:** **F = ma**. F is the **net** force (N), m the mass (kg), a the acceleration (m/s²).
- Rearranged: a = F ÷ m and m = F ÷ a.
- Double the net force, double the acceleration. Double the mass, half the acceleration.
- The acceleration points the same way as the net force.

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**What acceleration does a net force of 30 N give a 6 kg trolley?**

* a = F ÷ m = 30 ÷ 6 = 5 m/s², in the direction of the net force.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: Next: Newton's third law (node 5), then free body diagrams with several forces (node 6) and quantitative problems (node 7). In class: a trolley pulled by hanging masses (move masses from the trolley to the hanger to keep total mass constant), with light gates or a motion sensor. -->