What it does
A free-body diagram is a sketch of one body on its own with an arrow for every force acting on it. It is the first step in almost every mechanics problem, and the step where most marks are lost: a force is forgotten, or something that is not a force gets drawn in.
This page gives you six classic set-ups. For each one you pick a body, tick the forces you think act on it, and press Check my diagram. The page tells you what is missing, what does not act in this set-up, and what is not a force at all (a “force of motion”, or ma drawn as if it were a force). Then Show the answer draws the correct diagram to scale with the size of each force, and the Solve it card works out the acceleration, tension, normal force, friction or contact force with Newton’s second law, step by step.
The set-ups are: pulling a box along a rough floor with a rope at an angle; a block on a rough slope; a person on bathroom scales in a lift; pushing two blocks along a smooth floor; a block on a rough table tied over a pulley to a hanging block; and an Atwood machine, two blocks hanging over one pulley.
It follows Class 11 Physics, laws of motion (Newton’s laws, free-body diagrams, equilibrium of a particle, connected bodies, friction) and the Class 9 Science ideas of balanced and unbalanced forces. For a single block with friction, try friction ramp; to add forces at angles, use vector adder; and for pushes and momentum on the flat, see newton's laws sandbox.
How to use it
- Choose a set-up and set its masses, pull, angle, friction or lift acceleration with the sliders.
- When there are two blocks, choose which body you are drawing.
- Tick the forces on that body. Your arrows appear in the box below as you tick.
- Press Check my diagram. Fix anything missing or extra, or press Show the answer.
- Read Solve it: the equation for each body, then the result, and a final check that the forces on the chosen body really add up to m a.
Worked example
Open the page: a 5 kg box pulled with 30 N at 30° above the floor, μ = 0.2. The forces on the box are its weight (49 N down), the normal force from the floor, the pull, and friction backwards. Four forces; nothing else.
Up and down: N + 30 sin 30° = 49, so N = 34 N (less than the weight, because the rope lifts a little). Along the floor: 30 cos 30° = 25.98 N forward, friction μN = 0.2 × 34 = 6.8 N back, so a = (25.98 − 6.8) ÷ 5 = 3.84 m/s².
Switch to the Atwood machine with 3 kg and 5 kg: a = (5 − 3) × 9.8 ÷ 8 = 2.45 m/s² and T = 2 × 3 × 5 × 9.8 ÷ 8 = 36.75 N, between the two weights (29.4 N and 49 N), as it must be.
Tips
- Only two kinds of force act: gravity (at a distance) and contact forces (from anything touching the body: a surface, a string, your hand).
- The force that one block exerts on another, and the other’s push back, are a third-law pair; they act on different bodies, so only one of them goes on each diagram.
- ma is not a force. It is what the forces add up to.
FAQ
Why do the scales in a lift read more when it speeds up going up? The floor has to push you up harder than gravity pulls you down to give you an upward acceleration: N = m(g + a). Scales measure that push.
Why is the tension in an Atwood machine not equal to either weight? If it equalled the lighter weight, nothing would lift it; if it equalled the heavier, nothing would pull it down. It has to be in between for both to accelerate.
Is anything stored? No. Everything is worked out in your browser and nothing is saved or sent.
Where the numbers come from
- Newton's second and third laws applied body by body, with friction up to μN, for standard set-ups: Atwood machine a = (m₂ − m₁)g/(m₁ + m₂), T = 2m₁m₂g/(m₁ + m₂); apparent weight in a lift N = m(g + a). Standard school physics found in any textbook. g = 9.8 m/s² (rounded).
- Checked by adding every body's forces as x-y vectors on 3000 random set-ups (they must equal m a in the direction of motion) and against hand-worked examples.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.