Forces · Contrast
Balanced and unbalanced
Two identical books have the same weight pulling them down. One is sitting on a table and one is falling. The difference is not the weight.
Start here
The table is holding up 8 N and nobody notices.
A 0.8 kg book weighs about 8 N — mass in kilograms × 10 N/kg. Rest it on a table and it stays. Hold it out and let go and it drops. Its weight was 8 N the whole time.
So what is different about the forces on the book on the table?
There is a second force. The table is squashed by an amount too small to see and pushes back up with 8 N — exactly matching the weight, so the resultant is 0 N and nothing changes. Take the table away and the 8 N has nothing to cancel it.
Balanced means the forces along a line add up to a resultant of 0 N, so nothing about the motion changes. Unbalanced means something is left over, and whatever is left over is what changes the motion.
At the bench · the support rig
Change what is holding it up
Change a control to begin
Commit first. A 2 kg mass hangs from a spring and stays still. How hard is the spring pulling up?
What is holding it up
2 kg
Weight, pulling down
—
Push or pull, upwards
—
Resultant
—
Verdict
—
The relationship · a beam, not a triangle
Same length, opposite ways, nothing left over.
This is a beam and not a triangle, because the two forces are being subtracted from one another, never multiplied. Nothing here has a formula triangle, and putting one on it would teach a relationship that does not exist.
At rest and staying at rest: upward force = weight. So the upward force is the weight, in newtons.
weight in N = mass in kg × 10 N/kg
balanced: resultant = 0 N
unbalanced: resultant = bigger force − smaller force
Worked example · one step at a time
A 3 kg toolbox rests on a shelf. How hard does the shelf push up?
Step 0 of 5
Convert
3 kg stays 3 kg
The mass is already in kilograms, which is what × 10 N/kg needs, so there is nothing to convert.
Formula
upward force = weight
It is at rest and staying at rest, so the two forces are equal.
Insert
upward force = 3 kg × 10 N/kg
Weight in newtons is mass in kilograms × 10 N/kg.
Fine-tune
3 × 10 = 30
Kilograms times newtons per kilogram leaves newtons.
Answer
upward force = 30 N, upwards
Same size as the weight, opposite direction.
Worked example · one step at a time
A 250 g book rests on the same shelf. How hard does the shelf push up?
Step 0 of 5
Convert
250 g ÷ 1000 = 0.250 kg
× 10 N/kg wants kilograms, and a gram is a thousandth of one, so divide by 1000.
Formula
upward force = weight
At rest and staying at rest, so the two forces are equal.
Insert
upward force = 0.250 kg × 10 N/kg
The converted mass goes in. The 250 never does.
Fine-tune
0.250 × 10 = 2.5
Kilograms times newtons per kilogram leaves newtons.
Answer
upward force = 2.5 N, upwards
Insert 250 instead of 0.250 and the shelf comes out pushing a thousand times too hard.
Your turn · the same five steps
Your rig: 2.0 kg, resting on a table top.
Write all five lines before you check. The numbers are the ones your own rig is showing — and which relationship you need depends on whether it balances.
The five lines, marked
Convert
2.0 kg stays 2.0 kg
The mass is already in kilograms, which is what × 10 N/kg needs, so there is nothing to convert.
Formula
upward force = weight
It is at rest and staying at rest, so the two are equal.
Insert
upward force = 2.0 kg × 10 N/kg
Weight in newtons is mass in kilograms × 10 N/kg.
Fine-tune
2.0 × 10 = 20
Kilograms times newtons per kilogram leaves newtons.
Answer
upward force = 20 N, upwards
And the resultant is 0 N, which is why nothing happens.
The five lines give 20 N, and the arrows on the rig are drawn to match.
A 400 g mug sits still on a table. How hard does the table push up?
This one needs the Convert line to do some work.
The five lines, marked
Convert
400 g ÷ 1000 = 0.400 kg
× 10 N/kg wants kilograms, so divide the grams by 1000.
Formula
upward force = weight
Still and staying still, so the two forces are equal.
Insert
upward force = 0.400 kg × 10 N/kg
The converted mass goes in. The 400 never does.
Fine-tune
0.400 × 10 = 4
Kilograms times newtons per kilogram leaves newtons.
Answer
upward force = 4 N, upwards
Insert 400 instead of 0.400 and the table comes out pushing with 4000 N.
The five lines give 4 N upwards. The whole question turned on the first one.
Key fact
Balanced forces give a resultant of 0 N, so nothing about the motion changes — which is why a stretched spring or a squashed surface holding something at rest must be pushing back with exactly the weight, in newtons.
Think again
“If something is not moving, there are no forces on it.”
A resultant of 0 N and no forces at all look identical from a distance, and they are completely different situations. Hang a heavier and heavier load from a rope and nothing appears to happen — until the rope snaps, which is not something that happens to an object with no forces on it. Every bridge, chair and shelf you have ever used is holding a load in balance, and every one of them has a load it cannot hold. The forces are there; they are cancelling.
“Balanced forces mean the object is stopped.”
Balanced means no change, not no motion. A car at a steady 70 miles an hour on a motorway has a resultant force of 0 N: the engine's forward push exactly matches the air resistance and friction pushing back. Take your foot off the accelerator and the forces stop being balanced, and the car slows. A skydiver at terminal velocity is falling at a constant 55 metres per second with balanced forces. Balanced forces are the reason things carry on doing whatever they were doing, which is the whole subject of the next lesson.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
A 4 kg box sits still on a bench. What is the upward force from the bench?
Rung 2 · The one that catches people
A lorry is driving along a motorway at a steady 25 m/s. What can you say about the forces on it?
Rung 3 · Explain
A 2 kg bag of flour hangs from a spring and does not move. Explain, using both forces, why the spring stops stretching where it does.
Rung 4 · Take it somewhere new
A lift with a total mass of 500 kg hangs from a cable. The cable can pull with up to 6 000 N. Work out whether the lift is safe at rest, and explain what would have to happen to the forces for the lift to start moving upwards.
Key note
Forces on an object are balanced when they cancel to a resultant of 0 N, and unbalanced when something is left over. Anything held at rest by a spring or a surface is in balance, so the upward force must equal the weight — mass in kilograms × 10 N/kg. Balanced does not mean stationary; it means nothing is changing.
Going further
How does a table know how hard to push? It does not, and it does not need to. Every solid is a lattice of particles held together by forces that behave like tiny stiff springs. Put a book on the table and the top layer of particles is pushed a little closer to the layer below — a squash far too small to see, but real — and squashed springs push back. Add more load and they squash further and push back harder, and this continues automatically until the push matches the load. That is why the answer is always exactly the weight rather than approximately: the surface stops squashing at the point where the two are equal, and stays there. It is the same mechanism as the spring in the bench above, with a much shorter stretch.
It also explains why every support has a breaking point. Squash those particle springs far enough and the lattice fails — the paper tears, the shelf snaps, the ice gives way — and beyond that point the surface cannot supply the force needed, so the forces stop being balanced and the load goes through. Engineers do not design a bridge to be strong; they design it so that the largest load it will ever carry still leaves it in balance, with a margin. A structure that is in balance is doing its job, silently, and the failure is what happens when the arithmetic runs out.
Before this lesson
Connects to
At GCSE this becomes
- Resultant forces, equilibrium, Newton's first law, and terminal velocity.
Where to next
Ask Mr Badmus AI
Not sure whether a situation counts as balanced?
Weight in newtons is taken as mass in kilograms × 10 N/kg throughout. The support rig shows only the vertical forces, and the sheet of paper is given a made-up breaking point of 2 N so that failure is something you can reach; a real sheet depends on its size, its fibres and how it is held.
Lesson content © MrBadmusAI.