Free-Body Diagram Worksheet Generator
A free-body diagram shows one object and every force on it — and only the forces on it. This sets scenes of three kinds: on a level surface, hanging from strings or a cable, and on a slope, from a box at rest on a table to a sign on two wires and a crate pulled up a ramp. Each asks for the diagram and a size: the push, the tension, the acceleration. The answers draw the forces to scale from a dot, give each one's size and direction, and name one force that does not belong on the diagram because it acts on something else.
What this generator does
Builds each scene from its physics, as forces with right and up components in newtons, then checks the diagram independently: the forces must add up to mass × acceleration, a normal force must push at right angles to its surface, friction must run along the surface against the motion (and equal μN when sliding), strings must pull, and no force on the diagram may be exerted by the object itself.
How to use this tool
- Choose a level, the value of g your class uses, and how many scenes.
- Press Make the sheet. Each scene is drawn with its surfaces and strings but no forces.
- Show the answers to see the forces drawn to scale, their sizes and the working.
- Print the sheet and answers, or type a sheet code to make the same sheet again.
Understanding the controls
- Level
- Gentle: a box at rest on a table, a lamp on one cord, a crate pushed at a steady speed. Standard: an accelerating sledge, a crane load accelerating up or down, a block at rest on a slope. Stretch: a sign on two wires, a crate pulled up a slope, a suitcase pulled by a strap at an angle.
- Gravitational field strength
- g = 9.8 N/kg or 10 N/kg, whichever your course uses. It is stated on every scene.
- How many scenes
- 3 or 6, taking the level's three kinds in turn. Two print to a page, one at large print.
- Sheet code
- Leave empty for a fresh sheet from the browser's secure generator; with a code, the same code and settings make the same sheet again while the generator is unchanged.
Worked examples
- Resting on a slope
- A 10 kg block at rest on a 30° slope, g = 9.8: weight 98 N straight down; normal force 98 cos 30° = 84.9 N at right angles to the slope; friction 98 sin 30° = 49 N up the slope.
- Not on the diagram
- A box resting on a table pushes down on the table. That force acts on the table, so it belongs on the table's diagram, not the box's.
Common use cases
- Practice drawing free-body diagrams before resolving forces
- Homework on friction, normal force and tension with stated assumptions
- Showing why the table's push and the box's push on the table are not on the same diagram
How this generator works
Masses are whole kilograms. A scene at rest or at a steady speed has no resultant force; an accelerating one has a resultant of mass × acceleration. On a slope the weight is resolved along and across it (N = W cos θ, the along-slope part W sin θ). Two wires are solved from the two balance equations. A sliding object's friction is μ times the normal force; a resting one's takes whatever size holds it, which needs μ of at least tan θ, and the scene says so. The checks are made on the finished forces, not on the formulas that made them.
Randomness and fairness
Scenes come from the browser's secure generator, or a seeded one when you type a code. Codes are deterministic, not cryptographic, and not a secret.
For how randomness is produced across the whole site, see how Generate Random works.
Assumptions this tool makes
- Every object is treated as a single point, strings, ropes and cables are light, and air resistance is ignored.
- Sliding friction is μ × the normal force; friction on a resting object is only as large as needed to hold it.
Limitations and good to know
- Diagrams, not experiments: the numbers are worked from the stated assumptions, not measured.
- Objects are points, so there is nothing about turning effects, moments or where on the object a force acts.
- Sizes are given to 1 decimal place; working with rounded values can differ in the last figure.
- Static friction is only ever as large as needed; the questions do not ask whether a block is about to slip.
Common mistakes
- Drawing the object's push on the table as well as the table's push on the object
- Only forces acting ON the object go on its diagram. Its push on the table acts on the table.
- Making the normal force on a slope equal to the weight
- Only the part of the weight across the slope is balanced by the normal force: N = W cos θ.
- Drawing an extra 'force of motion' in the direction of travel
- Moving at a steady speed needs no resultant force. Every force on the diagram must be exerted by something you can name.
Privacy and your data
Sheets are built in your browser. With analytics consent, a count records how many scenes a sheet had; the sheet and any code are not sent.
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