Extension: Newton's Second Law, Qualitative
You'll be able to predict which object accelerates more from a given push.
In 2020, JAXA's Hayabusa2 capsule re-entered Earth's atmosphere at 12 km/s, a speed only possible because its tiny 300 N thruster had been pushing a spacecraft that got lighter as it burned fuel for 6 years.
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Q1 · Push a shopping trolley gently vs as hard as you can. What's different about how it moves?
Q2 · Would you rather push a shopping trolley full of bricks or one full of feathers? Why?
● Know
- That applying more force produces more acceleration
- That more mass produces less acceleration for the same force
- The names: Newton's Second Law, force, mass, acceleration
● Understand
- Why heavier objects accelerate less when pushed with the same force
- How force and acceleration are proportional (same direction)
- Why we describe this conceptually before using the formula
● Can do
- Predict which object accelerates more from a given push
- Rank scenarios by acceleration (qualitative)
- Apply the concept to Australian sporting and vehicle examples
Push a friend on a skateboard gently. Now push twice as hard. They accelerate twice as fast. That's Newton's Second Law in action, more force means more acceleration.
There are two sides to this law:
- Relationship 1, Force and acceleration: If you double the force on an object (keeping its mass the same), you double its acceleration. Push three times as hard → accelerate three times as fast. Force and acceleration are proportional when mass is fixed.
- Relationship 2, Mass and acceleration: If you double the mass of an object (keeping the force the same), you get half the acceleration. More mass → harder to accelerate → less acceleration.
The first relationship is easy to accept: push harder, get more. The second one is where the previous lesson pays off, because on its own "more mass gives less acceleration" sounds like a fact to memorise. It is not. It is inertia, seen from the other side. Inertia is an object's resistance to any change in its motion, and it grows with mass because mass counts how much matter has to be got moving. Acceleration is a change in motion. So a larger mass means a larger resistance to exactly the thing your force is trying to produce, and the same push therefore buys you less of it. Newton's First Law told you that objects resist change; the Second Law is the same idea with a number attached to how much.
Both relationships work at the same time, which is why you cannot predict an acceleration from either quantity alone. A very light object pushed hard accelerates a great deal. A very heavy object pushed lightly barely accelerates at all. But a heavy object pushed very hard can out-accelerate a light one pushed gently, which is why a 2,000 kg sports car beats a bicycle away from the lights despite having a hundred times the mass. Whenever someone asks which of two objects accelerates more, your first question should be whether the forces are the same, because if they are not, the mass comparison on its own settles nothing.
Key point for Year 7: You do NOT need to calculate anything. The conceptual rule, more force or less mass → more acceleration, is the goal for now. In Year 9 you will use the formula F = ma to calculate exactly how much.
Text description
- Same mass (2 kg): a small force gives little acceleration; a big force gives big acceleration.
- Same force: a 1 kg mass gets lots of acceleration; a 10 kg mass gets little acceleration.
- F = m × a: force = mass × acceleration.
Newton's Second Law shows up everywhere you look in sport and transport:
- Tennis vs shot put: A tennis player can accelerate a tennis ball (57 g) dramatically with one swing. The same swing would barely move a shot put (7.26 kg), the huge mass difference means far less acceleration for the same force.
- Motorcycles vs semi-trailers: A motorcycle and a loaded semi-trailer may have similar engine power at low speed, but their masses are vastly different. The motorcycle (200 kg) accelerates off the mark; the semi-trailer (50,000 kg) takes a long time to build speed.
- Bathurst racing (Mount Panorama): Teams work incredibly hard to reduce car mass by grams, every kilogram removed means slightly more acceleration from the same engine force. Lighter cars accelerate faster from corners and achieve higher top speeds.
- AFL kick: A footballer applies roughly the same kicking force every time. Kick a standard football → it flies fast. Kick a waterlogged heavy football in the rain → much less acceleration, shorter kick.
The pattern is always the same: less mass → more acceleration from the same force.
You might wonder: why aren't we using F = ma right now? Here's the thinking:
- Patterns first, formula second. In science, understanding the relationship (more force → more acceleration) before plugging numbers in means the maths will actually make sense when you get there in Year 9.
- Rockets (a great example): A rocket burns fuel, which provides a large thrust force upward. As it burns fuel, the rocket gets lighter. Same thrust, less mass → more acceleration. That's why rockets accelerate faster as the launch progresses.
- Car safety: In a crash, a car decelerates suddenly. Airbags work by increasing the time over which your body slows down, this reduces your body's acceleration, which reduces the force on you. Newton's Second Law, saving lives.
- Preview: Force = mass × acceleration. When you study this in Year 9, every number you calculate will connect back to today's idea: force, mass and acceleration are linked.
Wrong: "Heavier objects always accelerate less." This is only true if the force is the same. Give the heavier object a proportionally larger force and it can accelerate just as much.
Right: For the same force, more mass → less acceleration. But if force also increases, acceleration can stay the same or increase.
Wrong: "More force always means faster in the end." Force produces acceleration, not speed. An object can have huge acceleration from rest and still be slower than one that's been accelerating for longer.
Right: Force → acceleration (rate of change of speed). Speed depends on how long that acceleration has been acting.
Wrong: "Newton's Second Law needs a formula to be useful." The conceptual version, more force, less mass → more acceleration, is already powerful enough to explain rockets, crashes, sport and engineering.
Right: The qualitative pattern is real science. The formula F = ma is how you quantify it, it comes later.
Rank these four scenarios from highest to lowest acceleration. Assume each push is the same unless stated. Explain your reasoning.
- A: Small ball pushed hard
- B: Large ball pushed gently
- C: Small ball pushed gently
- D: Large ball pushed hard
Show model answer
Model ranking: A → (C and D in either order or tied) → B
A: small mass with a large force gives the greatest acceleration. B: large mass with a small force gives the least. C and D are in the middle, but their relative order cannot be determined from the information given: C has a smaller mass and smaller force, while D has a larger mass and larger force. Which effect is stronger depends on the actual masses and forces, so C → D, D → C, or a tie is acceptable.
Two unloaded bikes, with no riders, have masses of 8 kg and 16 kg. Each experiences the same net forward force of 80 N. Before you see the answer: which bike has the greater acceleration? What happens if the net force on each bike doubles?
How close was your prediction?
Q1. A footballer kicks a soccer ball and a medicine ball with the same force. Explain which ball accelerates more and why, using Newton's Second Law. (2 marks)
Q2. A car engine produces a fixed force. What happens to the car's acceleration as it picks up a full load of passengers? Explain qualitatively. (3 marks)
Q3. Compare the acceleration of a racing car and a fully loaded truck, assuming both engines produce the same force. Explain your reasoning in terms of Newton's Second Law. (4 marks)
Answers
▾MCQ 1
C Force and acceleration are proportional. Double the force (same mass) → double the acceleration.
MCQ 2
C With no riders, the total masses are 8 kg and 16 kg. For the same net force, a = F ÷ m, so the 8 kg bike has twice the acceleration. A rider would add to the total mass and must not be ignored.
MCQ 3
B A bowling ball has far greater mass than a tennis ball, golf ball or ping-pong ball. For the same applied force, greater mass → less acceleration.
MCQ 4
C As the rocket burns fuel, its mass decreases. The same engine thrust now acts on a lighter rocket → greater acceleration. This is Newton's Second Law: acceleration = force ÷ mass.
MCQ 5
D Newton's Second Law: acceleration depends on BOTH the applied force AND the object's mass. Changing either will change the acceleration.
Short Answer 1
Model answer: The soccer ball accelerates more (1 mark). The soccer ball has much less mass than the medicine ball (1 mark). According to Newton's Second Law, for the same force, less mass produces more acceleration.
Short Answer 2
Model answer: When passengers are added, the total mass of the car increases (1 mark). The engine force remains the same (1 mark). According to Newton's Second Law, more mass with the same force means less acceleration, the car accelerates more slowly when fully loaded (1 mark).
Short Answer 3
Model answer: A racing car has much less mass than a fully loaded truck (1 mark). If both engines produce the same force, the racing car will have far greater acceleration (1 mark) because Newton's Second Law states that acceleration depends on force and mass, less mass means more acceleration from the same force (1 mark). The loaded truck has enormous mass so even with the same engine force it barely accelerates by comparison (1 mark).
The hook at the start of this lesson described a rocket getting faster and faster as it burns fuel, not because it produces more thrust, but because it gets lighter. Can you now explain why?
Use Newton's Second Law to explain the rocket's increasing acceleration, and then connect it to why you'd rather push a trolley of feathers than a trolley of bricks. Use the words force, mass and acceleration at least once each.
- Newton's Second Law links three quantities: the force on an object, its mass, and the acceleration that results. Change either of the first two and the third changes.
- For a fixed mass, force and acceleration are proportional: double the push, double the acceleration. For a fixed force, more mass means less acceleration, because inertia is what resists the change.
- You are not expected to calculate anything yet. The pattern (more force or less mass gives more acceleration) is enough to explain rockets, racing cars and a waterlogged football, and the formula F = ma comes in Stage 5.