Newton's laws and F = m·a

Lesson page: echoesof.science/school/forces-and-motion/ages-15-16/ · Pupil worksheet: echoesof.science/school/forces-and-motion/ages-15-16/print/

Learning aims

Use free-body diagrams and the idea of net force.
State and apply Newton's three laws.
Calculate with F = m·a and W = m·g, with correct units.
Investigate a ∝ F at constant mass and evaluate the uncertainties.

Lesson plan

Time	Activity
5 min	Starter: why does a passenger lurch forwards when a bus brakes? (inertia)
10 min	Read the text; worked examples of F = m·a and W = m·g.
25 min	Trolley experiment in groups; plot a against F.
5 min	Discuss the gradient and sources of error.
5 min	Quiz, or the game as homework.

Materials for the experiment

Dynamics trolley and runway (or a smooth bench)
Pulley clamped to the end of the bench
String
Slotted masses on a hanger (e.g. 5 × 20 g)
Light gates and data logger, or a stopwatch and metre rule
Sand tray or padded box to catch the masses
Balance

Safety: Put a sand tray or padded box under the hanging masses and keep feet away. Clamp the pulley firmly, and stop the trolley with a buffer at the end of the runway. Don't overload the hanger.

Common misconceptions

Pupils may think…	Actually…
A constant force is needed to keep something moving at a constant speed.	With zero net force, velocity is constant; a driving force is only needed to cancel friction and drag.
Action and reaction forces cancel out.	They act on different objects, so they cannot cancel each other.
Mass and weight are the same thing.	Mass (kg) is the same everywhere; weight (N) = m·g depends on where you are.

Worksheet answers

Weight (down) and the normal contact force from the table (up), equal in size. The net force is zero, so the acceleration is zero.
a = (15 − 0)/10 = 1.5 m/s²; F = m·a = 1200 × 1.5 = 1800 N.
Gradient = 1/m, so m = 1/gradient. It is usually close to, but a little larger than, the measured mass, because friction is not fully compensated (or the string and pulley add effects), and timing errors.
She pushes the water backwards (action); the water pushes her forwards with an equal and opposite force (reaction).

Quiz answers

A net force of 12 N acts on a 3 kg trolley. What is its acceleration? 4 m/s². a = F/m = 12 / 3 = 4 m/s².[3]
What is the weight of a 50 kg student on Earth (g = 9.8 m/s²)? About 490 N. W = m·g = 50 × 9.8 = 490 N.[3]
The same 50 kg student on the Moon (g = 1.67 m/s²) has a mass of… 50 kg. Weight changes with g, but the mass stays 50 kg; the weight would be about 84 N.[3]
A spacecraft far from any planet switches off its engines. What happens? It keeps moving in a straight line at constant speed. With no net external force, velocity stays constant.[2][4]
Which unit is the same as a newton? kg·m/s². 1 N = 1 kg·m/s².[3]
A rocket pushes on its exhaust gas. The reaction force acts… on the rocket, pushed by the gas. The gas pushes on the rocket: the pair of forces acts on different objects.[4]

Going further

Repeat the experiment keeping the force constant (one mass on the hanger) and adding masses to the trolley. Plot a against 1/m. What shape do you expect, and why?

Sources used in this lesson

[1] Physics, 4.1 Force (OpenStax, Rice University): reliability High
[2] Physics, 4.2 Newton's First Law of Motion: Inertia (OpenStax, Rice University): reliability High
[3] Physics, 4.3 Newton's Second Law of Motion (OpenStax, Rice University): reliability High
[4] Rocket Principles (Newton's laws of motion) (NASA Glenn Research Center): reliability High
[5] Newton's First and Second Laws of Motion (NASA Glenn Research Center): reliability High
[7] What is Drag? (NASA Glenn Research Center, Beginner's Guide to Aeronautics): reliability High

Full list with links and a note on each source's reliability: echoesof.science/school/forces-and-motion/sources/

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