GCSE · Physics · Edexcel · Spec 1PH0

Newton's second law F = ma

Push an empty shopping trolley and it shoots off. Push a full one just as hard and it barely moves. Same push, different result — one short equation explains why.

Physics · Forces

Which force is F? Find the resultant first

Three objects, each with more than one force on it. Switch between them and watch the net-force readout — not the longest arrow.

Resultant force · F = ma

Net force0 N

A box sitting on the floor. Its weight pulls down with 500 N and the floor pushes up with 500 N (the arrow labelled Normal). Two forces act, but 500 − 500 = 0 N.

Selected scenario

Forces cancel

Net force

0 N

Motion

No acceleration

No acceleration. The forces cancel, so the resultant is zero — and zero resultant force means zero acceleration.

Watch out: The longest arrow is not F. F is what's left after you add the forces going one way and subtract the forces going the other.

Physics · Resultant force

Speed up, slow down, or neither?

Each object is moving to the right. Sort it by what its resultant force will do.

Still to sort

Speeds up (0)

Resultant points the same way as the motion.

Where the line is: It is the direction of the resultant that matters, not which single force is largest.

No acceleration (0)

The forces cancel: resultant 0 N.

Where the line is: Forces are still acting — they just add up to zero, so a = 0.

Slows down (0)

Resultant points against the motion.

Where the line is: A backwards resultant makes the object decelerate even though it is still moving forwards.

5 of 5 still to sort.

Every object here is already moving to the right. Work out the resultant in your head, then decide what it does to the motion.

Watch out: Still moving forwards does not mean speeding up. A resultant pointing backwards slows an object down even while it carries on forwards.

Physics · Force and acceleration

Double the force, double the acceleration

resultant force: 2/10. Resultant force 200 N. Acceleration 1.0 m/s²

Resultant force200 NAcceleration1.0 m/s²

A go-kart and driver with a total mass of 200 kg. The bar is the resultant force; the acceleration readout is F ÷ m. Try 200 N, then 400 N, then 800 N.

Watch out: This lockstep only holds while the mass stays the same. Change the mass and the whole relationship changes.

Predict, then check

Same push, different trolley. Commit before you look.

The same 60 N resultant force acts on an empty 20 kg trolley and then on a loaded 60 kg trolley. What happens to the loaded trolley's acceleration?

F = m × a — three ways round

Cover the quantity you want. Side by side means multiply; one above the other means divide.

Tap the quantity you want to find. The triangle shows you the formula.

Cover resultant force, mass or acceleration to reveal its rearranged formula, then plug in numbers to solve.

Braking car — a deceleration, step by step

Problem

A car of mass 1200 kg is moving forwards. Its engine gives a driving force of 900 N forwards. The brakes give a force of 3.3 kN backwards, and air resistance is 600 N backwards. Calculate the car's acceleration.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

F = m × a

F is the resultant force — the overall effect of every force on the object.

What you need to know

Acceleration is directly proportional to the resultant force and inversely proportional to the mass.
Newton's second law: resultant force = mass × acceleration, F = m × a, with F in newtons (N), m in kilograms (kg) and a in metres per second squared (m/s²).
F is the resultant force: add the forces acting one way along the line and subtract those acting the other way.
Rearranged: a = F ÷ m and m = F ÷ a. Convert kN and MN to newtons before you substitute.
A resultant force in the direction of motion speeds an object up; a resultant force against the motion slows it down (a deceleration).

The big picture

The acceleration of an object depends on two things: the resultant force on it and its mass. Double the resultant force and the acceleration doubles; put the same force on a bigger mass and the acceleration is smaller. The link is F = m × a, where F is always the resultant force — found by combining every force along the line — and a resultant against the motion makes the object slow down.

Key points

1F in F = m × a means the resultant force — never just the largest or the driving force.

2To find the resultant along a line: add the forces one way, subtract the forces the other way, and note the direction.

3Same mass: double the resultant force, double the acceleration.

4Same resultant force: bigger mass, smaller acceleration — a heavier object is harder to accelerate.

5Resultant with the motion → speeds up; resultant against the motion → slows down; resultant zero → no acceleration.

6Units: N, kg, m/s². 1 kN = 1000 N and 1 MN = 1 000 000 N.

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Worked example

Problem

A boat's engine pushes it forwards with 3000 N. Water resistance acts backwards with 600 N. The boat accelerates at 0.8 m/s². Calculate the mass of the boat.

⚠ Watch out

Putting the driving force (or whichever force is biggest) into F = m × a. F is the resultant: subtract the forces acting the other way first, or your acceleration comes out too big.

🧠

Memory hook

Arrows first, one arrow left, THEN F = m × a. The equation only ever gets the arrow that's left over.

✓

Check yourself

A 50 kg crate is pushed with 180 N while friction pulls back with 80 N. What is its acceleration? (Resultant 100 N forwards, so a = 100 ÷ 50 = 2 m/s².)

Flashcards

(12)

In F = m × a, what does F stand for?

The resultant force — the overall effect of all the forces acting on the object, not any single one of them.

What are the units of F, m and a?

F in newtons (N), m in kilograms (kg), a in metres per second squared (m/s²).

Rearrange F = m × a to find the acceleration.

a = F ÷ m

Rearrange F = m × a to find the mass.

m = F ÷ a

How do you find the resultant of several forces along a line?

Add the forces acting in one direction, subtract the forces acting in the opposite direction, and keep track of which way the answer points.

The resultant force points the same way the object is moving. What happens?

It speeds up.

The resultant force points opposite to the way the object is moving. What happens?

It slows down — it decelerates, even though it is still moving forwards for now.

The mass stays the same and the resultant force doubles. What happens to the acceleration?

It doubles too. Whatever you do to F, you do to a — as long as m stays fixed.

Two objects feel the same resultant force. Which one has the smaller acceleration?

The one with the greater mass — it is harder to accelerate.

State Newton's second law in words.

An object's acceleration is directly proportional to the resultant force on it and inversely proportional to its mass.

Convert 4.5 kN and 2 MN into newtons.

4.5 kN = 4500 N; 2 MN = 2 000 000 N. Kilo means × 1000, mega means × 1 000 000.

Forces act on an object but the resultant is 0 N. What is its acceleration?

Zero: a = 0 ÷ m = 0. The forces are real, but they cancel.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Which force is F? Find the resultant first

Speed up, slow down, or neither?

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