← Teacher guide

How hard do you need to push?

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).

Year 10 Physics · Newton's laws · about 30 minutes · Open the student lesson

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

Students will be able to

Timing

Engage and Explore 8 min · Explain 9 min · Practise 4 min · Evaluate 3 min · Typical adds 4 min, Wider about 2 min

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.

Running the lesson

  1. Engage: put the four predictions on the board; come back after Explore.
  2. Explore: ask what push hit target 1 (8 N) and target 2 (16 N). Write F, m, a in a table.
  3. Explain: students should say the rearrangement aloud for each number check.
  4. In your own words: the doubling paragraph is the evidence of the qualitative relationship.

The hard part (on purpose)

Using the net force, not the push, in F = ma. When a student uses the push, ask whether anything is pushing back.

When students get stuck

What you will seeA question to askThe fix
A student uses the push instead of the net force.Is anything pushing back?Subtract opposing forces first: F in F = ma is the net force.
A student confuses mass and weight in F = ma.Which is in kilograms?Mass (kg) goes in F = ma. Weight is a force (N).
A student thinks doubling mass halves the force needed.For the same acceleration, what did you need for 8 kg compared with 4 kg?Twice the force. Same force on double the mass gives half the acceleration.

Answers to the checks

  1. Engage: double the mass: 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.
    2 m/s². Doubling the mass halves the acceleration for the same net force: a = F ÷ m.
  2. Target 1: Give the 4 kg trolley an acceleration of 2 m/s².
  3. Target 2: Now double the mass to 8 kg and get the same acceleration, 2 m/s².
  4. The rule: For 4 kg you needed 8 N; for 8 kg, 16 N. What rule links force, mass and acceleration?
    Force = mass × acceleration (F = ma)
    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.
  5. Find the force: What net force gives a 1200 kg car an acceleration of 3 m/s², in N?
    3600
    F = ma = 1200 × 3 = 3600 N.
  6. Find the acceleration: A net force of 50 N acts on a 10 kg box. Its acceleration, in m/s²?
    5
    a = F ÷ m = 50 ÷ 10 = 5 m/s².
  7. Find the mass: A net force of 600 N gives a sprinter an acceleration of 10 m/s². Her mass, in kg?
    60
    m = F ÷ a = 600 ÷ 10 = 60 kg.
  8. Net force: A 2 kg box is pushed with 10 N against 4 N of friction. What force goes into F = ma?
    The net force, 6 N
    Net force 10 − 4 = 6 N, so a = 6 ÷ 2 = 3 m/s².
  9. Units: Match each quantity to its unit.
    Force (F) → D. newtons (N); Mass (m) → B. kilograms (kg); Acceleration (a) → C. metres per second squared (m/s²); Velocity (v) → A. metres per second (m/s)
    F = ma only works with these units: mass in kg (not g), acceleration in m/s² (not m/s).
  10. Double, half or same: What happens to the acceleration?
    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
  11. 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?
    18
    Three times the force, three times the acceleration: 18 m/s².
  12. 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?
    5
    Δv ÷ Δt = 20 ÷ 4 = 5 m/s² (backwards).
  13. Braking force: What braking force does that need, in N?
    7500
    F = ma = 1500 × 5 = 7500 N, backwards.
  14. 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…
    bigger
    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.
  15. 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 straight line through the origin (gradient 1 ÷ mass)
    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.

Stretch and support

Stretch: Rockets lose mass as they burn fuel. With the same thrust, what happens to their acceleration during the launch?

Support: Give the formula triangle (F at the top, m and a below) with one worked example of each rearrangement.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient science coach for a Year 10 student in Australia. Help me understand ONE idea only, from the lesson "How hard do you need to push?".

The idea: Newton's Second Law — F = ma: I can apply F = ma to calculate force, mass or acceleration in single-force scenarios and explain qualitatively how changing mass or force affects acceleration.

What understanding looks like:
- Correctly applies F = ma to solve for force, mass or acceleration in a single-force scenario
- Uses correct units (N, kg, m/s²) and maintains direction consistency
- Explains qualitatively how doubling force or mass affects acceleration

Mistakes students often make here:
- A student uses the push instead of the net force.
- A student confuses mass and weight in F = ma.
- A student thinks doubling mass halves the force needed.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- If I seem to be missing the idea that comes before this one (Acceleration as a defined vector quantity), check it quickly, then come back.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "How hard do you need to push?".

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.

What each step is for

Where it 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.