Newton’s second law and the acceleration required practical
By Engr. Mehmood Kakar · Updated
Quick answer
Newton’s second law says the acceleration of an object is proportional to the resultant force on it and inversely proportional to its mass: F = m × a. In the required practical you pull a trolley with different forces (keeping the total mass the same), then with different masses (keeping the force the same), and measure the acceleration with light gates.
What the law says
A resultant force makes an object accelerate. The bigger the resultant force, the bigger the acceleration; the bigger the mass, the smaller the acceleration. Written as an equation, this is F = m × a, with force in newtons, mass in kilograms and acceleration in m/s².
The force in the equation is the resultant force: add the forces in one direction and subtract those in the other. A car with 3000 N of driving force and 1200 N of drag has a resultant force of 1800 N.
Higher tier students also need the idea of inertial mass: how difficult it is to change an object’s velocity, defined as m = F ÷ a.
F = ma worked questions
A resultant force of 2.0 N acts on a trolley of mass 0.80 kg. Calculate its acceleration.
- Rearrange: a = F ÷ m
- a = 2.0 ÷ 0.80
- a = 2.5 m/s²
A car of mass 1200 kg has a driving force of 3000 N and drag of 1200 N. Calculate its acceleration.
- Resultant force: F = 3000 − 1200 = 1800 N
- a = F ÷ m = 1800 ÷ 1200
- a = 1.5 m/s²
A cyclist and bike, total mass 80 kg, accelerate at 0.60 m/s². What resultant force acts?
- F = m × a = 80 × 0.60
- F = 48 N
The required practical
The investigation has two parts:
- Part 1: change the force on an object of constant mass and measure the acceleration.
- Part 2: change the mass of an object pulled by a constant force and measure the acceleration.
The usual set-up is a trolley on a runway, pulled by a string that runs over a pulley at the end of the bench to a hanger with slotted masses. The weight of the hanging masses provides the pulling force (W = mg, so 100 g gives 0.98 N).
Method
- Set up the runway with a pulley at one end. Attach a string from the trolley over the pulley to a mass hanger.
- Put a card on the trolley and position two light gates along the runway, connected to a data logger.
- Part 1 (changing force): start with all the slotted masses on the trolley. Release the trolley from the same point each time and record the acceleration. Move one mass from the trolley to the hanger and repeat, until all the masses are on the hanger.
- Part 2 (changing mass): keep the hanging mass the same. Add masses to the trolley one at a time, recording the acceleration each time.
- Repeat each reading and calculate a mean.
Why move the masses rather than add new ones? The hanging masses accelerate too, so they are part of the moving mass. Moving them from trolley to hanger changes the force but keeps the total mass the same, which is exactly what Part 1 needs.
Measuring the acceleration
Each light gate measures how long the card blocks the beam. Speed at a gate = card length ÷ time blocked. Then:
A 10 cm card blocks the first gate for 0.50 s and the second for 0.125 s. The trolley takes 0.50 s to travel between the gates. Calculate the acceleration.
- Speed at gate 1: u = 0.10 ÷ 0.50 = 0.20 m/s
- Speed at gate 2: v = 0.10 ÷ 0.125 = 0.80 m/s
- a = (v − u) ÷ t = (0.80 − 0.20) ÷ 0.50
- a = 1.2 m/s²
Without light gates, you can mark distances on the runway, time the trolley with a stopwatch and work out speeds, but human reaction time makes the results much less accurate.
Results and graphs
- Acceleration against force (constant mass): a straight line through the origin. Acceleration is directly proportional to resultant force.
- Acceleration against mass (constant force): a curve. Acceleration falls as mass rises: doubling the mass halves the acceleration.
- Acceleration against 1 ÷ mass: a straight line through the origin, which shows acceleration is inversely proportional to mass.
The F = ma simulation shows both effects: try doubling the force, then doubling the mass.
Errors and improvements
- Friction. Friction opposes the pull, so the resultant force is less than the hanging weight. Tilt the runway very slightly until the trolley rolls at a steady speed when given a push; then friction is balanced.
- Reaction time. Use light gates and a data logger instead of a stopwatch.
- Release. Release from the same point without pushing, so the starting conditions match.
- Repeats. Repeat and take a mean to reduce random error; spot and re-test anomalous results.
Practice
1. A 1500 kg car accelerates at 2.0 m/s². What resultant force acts on it?
F = m × a = 1500 × 2.0 → F = 3000 N
2. A 0.50 kg trolley is pulled by a resultant force of 1.5 N. Calculate its acceleration.
a = F ÷ m = 1.5 ÷ 0.50 → a = 3.0 m/s²
3. In Part 1 of the practical, which variables are independent, dependent and controlled?
Independent: the resultant (pulling) force. Dependent: the acceleration. Controlled: the total mass of trolley plus hanging masses, the runway and the release point.
4. A force of 12 N gives an object an acceleration of 4.0 m/s². What is its inertial mass? (Higher)
m = F ÷ a = 12 ÷ 4.0 → m = 3.0 kg
Frequently asked questions
What is Newton’s second law?
The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. As an equation: resultant force = mass × acceleration, F = m a.
Why do you move masses from the trolley to the hanger when changing the force?
The hanging masses accelerate along with the trolley, so they are part of the moving mass. Moving them from the trolley to the hanger changes the pulling force while keeping the total mass the same, so mass is a fair control variable.
How do light gates measure acceleration?
A card on the trolley cuts each light beam. The time it blocks a gate gives the speed there (card length ÷ time). With two gates, acceleration = change in speed ÷ time taken between the gates. A double-segment card through one gate works the same way.
What graph shows that acceleration is proportional to force?
A graph of acceleration against resultant force for a constant mass. If it is a straight line through the origin, acceleration is directly proportional to force.
What is inertial mass?
Inertial mass measures how difficult it is to change an object’s velocity. It is defined as the ratio of force to acceleration, m = F ÷ a. This is Higher tier on AQA.
Written by Engr. Mehmood Kakar
Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)
Checked against the AQA GCSE Physics (8463) specification on 15 November 2026.