A free body diagram (FBD) is a simple sketch that shows a single object with arrows representing every force acting on it. It is one of the most powerful tools in physics because it forces you to identify all forces before writing equations. Without an accurate FBD, even experienced physicists make errors in multi-step problems.
The key rule is to include only forces acting on the object - not forces the object exerts on other things. Each arrow should point in the direction the force acts and be labeled clearly. Once drawn, the diagram tells you directly which direction the net force points, which is the direction of acceleration.
Understanding Free Body Diagrams
A reliable diagram begins with choosing the object boundary. The object might be a book, a person, a cart, or a whole system of connected objects. Everything outside that boundary can interact with it.
List those interactions before drawing arrows. Earth provides gravitational attraction. A floor, wall, ramp, or hand provides contact forces.
A string provides a pulling force. Air or water can provide resistance. This method prevents a common mistake, which is drawing a force simply because an object is moving in that direction.
Motion is not a force. An object sliding right can have its largest force pointing left if it is slowing down.
Contact forces need careful thought because one contact can create more than one force. A surface pushes outward on an object, while friction acts along the surface. The push from the surface changes when other forces change.
For example, pressing down on a box makes the surface push harder. Pulling a box partly upward makes that push smaller. Static friction is especially easy to misunderstand.
It does not always have one fixed size. It takes the amount needed to prevent slipping, up to a maximum value.
If the required amount becomes too large, the object begins to slide and kinetic friction takes over. This is why a heavy box can remain still under a small push, then suddenly start moving when the push increases.
Connected objects should usually be drawn separately first. Consider a hanging mass attached by a rope to a cart. The rope pulls the cart toward the pulley and pulls the hanging mass upward.
These pulls are forces on different objects, so they belong on different diagrams. In a simple light rope over a low friction pulley, the tension is treated as having the same size throughout the rope. Real ropes can stretch and real pulleys can add friction, but introductory problems often ignore these effects.
Newton's third law helps with checking interactions. If a hand pushes a cart, the cart pushes the hand with equal size in the opposite direction. Those two forces never belong on the same object diagram.
After the forces are identified, choose directions that make the calculation simpler. On a ramp, one direction is usually along the slope and the other is perpendicular to it. Gravity can then be split into a part that tends to move the object down the slope and a part that presses it into the surface.
Write one force equation for each chosen direction. A zero total force means no acceleration in that direction, not necessarily no motion. In daily life, this appears when an elevator moves at steady speed, a car cruises on level road, or a picture hangs still from two wires.
Check the final result against the situation. A negative answer usually means the real direction is opposite to the direction first chosen. A normal force that comes out negative often signals that the object has lost contact with the surface.
Key Facts
- Weight (gravity) always points straight down:
- Normal force is perpendicular to the contact surface - not always vertical.
- Friction opposes the direction of motion (kinetic friction) or impending motion (static friction).
- Tension in a rope acts along the rope, away from the object.
- For equilibrium (constant velocity or at rest): of forces in every direction .
- On an incline, decompose weight into components parallel and perpendicular to the slope.
Vocabulary
- Free body diagram
- A diagram showing only the object of interest and all external forces acting on it as arrows.
- Normal force
- The contact force perpendicular to a surface that prevents objects from passing through each other.
- Friction force
- A contact force parallel to a surface that opposes relative sliding motion.
- Tension
- A pulling force transmitted through a string, rope, or cable.
- Equilibrium
- A state in which the net force on an object is zero, so it moves at constant velocity or stays at rest.
Common Mistakes to Avoid
- Including forces the object exerts on other things. Only include forces acting on the object being analyzed.
- Drawing the normal force as always vertical. On an inclined surface the normal force is perpendicular to that surface.
- Leaving out friction when an object is sliding. Kinetic friction always opposes the direction of motion.
- Using weight and normal force interchangeably. They are equal in magnitude only on flat, horizontal surfaces with no vertical acceleration.
Practice Questions
- 1 Draw a free body diagram for a 10 kg box sitting on a horizontal table. Label all forces and calculate the normal force.
- 2 A 5 kg block is on a frictionless 30° incline. Draw the FBD and find the acceleration down the slope.
- 3 A picture hangs from two wires that each make a 40° angle with the ceiling. Draw the FBD and write equations for equilibrium.