Why does a shopping trolley accelerate quickly with a small push, while a loaded truck needs a huge engine to get moving? The answer lies in one of the most important equations in physics: F = ma. In this lesson you will discover how force, mass and acceleration are linked, learn to perform simple calculations, and investigate the relationship experimentally.
Imagine pushing an empty shopping trolley and a full shopping trolley with the same force.
Write down your answers before reading on:
Force, mass and acceleration linked
Newton's second law tells us that the acceleration of an object depends on two things: how hard you push (the force) and how much stuff you are pushing (the mass).
The law is written as an equation:
F = ma
Where F is the net force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²).
This means two important things:
Working with F = ma at Stage 5
Before you calculate, check that your units match the SI system:
| Quantity | Symbol | Unit | Unit symbol |
|---|---|---|---|
| Force | F | newton | N |
| Mass | m | kilogram | kg |
| Acceleration | a | metres per second squared | m/s² |
The equation can be rearranged to find any one variable:
Worked example: A 500 kg go-kart is pushed with a net force of 250 N. What is its acceleration?
a = F ÷ m = 250 N ÷ 500 kg = 0.5 m/s²
Investigating force, mass and acceleration
A common classroom investigation uses a trolley on a runway pulled by a hanging mass. By changing either the pulling force (hanging mass) or the trolley mass, students can measure how acceleration changes.
Method outline:
Expected results: A graph of acceleration against force should give a straight line through the origin, showing that a ∝ F. A graph of acceleration against 1/mass should also give a straight line, showing that a ∝ 1/m.
"Heavier objects fall faster than light objects." No — in the absence of air resistance, all objects fall with the same acceleration (about 9.8 m/s² near Earth's surface). A hammer and a feather dropped on the Moon land together. Air resistance on Earth makes lighter objects with large surface areas fall more slowly.
"More force always means more acceleration, no matter the mass." Not necessarily. Acceleration depends on both force and mass. A small force on a tiny mass can produce a huge acceleration, while a large force on a massive object might produce only a small acceleration.
Australian Rules Football: When a player kicks a football, the force they apply and the mass of the ball determine its acceleration off the boot. A lighter ball (like a Sherrin) accelerates more for the same kick force than a heavier medicine ball would.
V8 Supercars: Engineers constantly balance force and mass. A lighter car with a powerful engine achieves greater acceleration. Race teams use carbon fibre and lightweight materials to reduce mass while maintaining structural strength and safety.
Road trains: Australia's long road trains can have a total mass exceeding 100 tonnes. Drivers must allow enormous stopping distances because the massive mass resists changes in motion — a direct consequence of F = ma. A small car can brake much more quickly because its smaller mass means the same braking force produces a larger deceleration.
1. According to Newton's second law, what happens to the acceleration of an object if the net force on it doubles while the mass stays the same?
2. A 10 kg object experiences a net force of 40 N. What is its acceleration?
3. Which set of units is correct for calculating with F = ma?
4. Two identical rockets are launched. Rocket A carries a 500 kg satellite; Rocket B carries a 1000 kg satellite. Both engines produce the same thrust. Which statement is true?
5. In a trolley investigation, a student keeps the pulling force constant and doubles the mass of the trolley each time. Which graph shape correctly shows acceleration against mass?
1. Explain what Newton's second law (F = ma) tells us about the relationship between force, mass and acceleration. Use the terms "directly proportional" and "inversely proportional" in your answer. 4 MARKS
2. A 1200 kg car accelerates from rest to 15 m/s in 5 seconds. Calculate the net force acting on the car. Show all working. 4 MARKS
3. Describe a practical investigation you could conduct to show that acceleration is inversely proportional to mass. Include the equipment you would use, the variables you would control, and how you would process your data. 4 MARKS
Go back to your Think First answer. Has your understanding changed?
C — If the net force doubles while mass stays constant, acceleration also doubles. This is because acceleration is directly proportional to force (a = F/m).
B — Using a = F ÷ m = 40 N ÷ 10 kg = 4 m/s².
D — The correct SI units are: force in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²).
A — Since a = F/m and the thrust (F) is the same for both rockets, the rocket with less mass (Rocket A) will have a larger acceleration. Mass and acceleration are inversely proportional when force is constant.
B — Acceleration is inversely proportional to mass (a ∝ 1/m). As mass increases, acceleration decreases. This produces a curved graph that falls as mass rises, not a straight line.
Model answer: Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. "Directly proportional" means that if the net force doubles (and mass stays the same), the acceleration also doubles. "Inversely proportional" means that if the mass doubles (and force stays the same), the acceleration halves. The equation F = ma combines both relationships: a larger force produces more acceleration, while a larger mass produces less acceleration for the same force.
Model answer: First, calculate acceleration using a = Δv ÷ Δt = (15 m/s − 0 m/s) ÷ 5 s = 3 m/s². Then use F = ma to find the net force: F = 1200 kg × 3 m/s² = 3600 N. The net force acting on the car is 3600 N.
Model answer: Equipment: dynamics trolley, runway, pulley, string, hanging masses, ticker timer or motion sensor, balance. Method: keep the pulling force constant by using the same hanging mass each time, but vary the mass of the trolley by adding known masses to it. Measure the acceleration for each trolley mass using the motion sensor. Control variables: pulling force, runway angle, surface type. Process data: plot a graph of acceleration (y-axis) against 1/mass (x-axis). If acceleration is inversely proportional to mass, this graph should be a straight line passing through the origin, confirming the relationship.
Test your knowledge in a rapid-fire quiz battle. Defeat the boss by answering questions correctly!
Tick when you have finished all activities and checked your answers.