Free Body Diagram

A free-body diagram is a simple sketch of one chosen object with every external force on that object drawn as an arrow. You use it to separate the object from the rest of the scene, so you can apply Newton's laws without mixing in forces that act somewhere else.

The fastest check is this: what is pushing or pulling on the object right now, and what is the source of that force? If you cannot name the source, the force probably does not belong on the diagram yet.

What a free-body diagram shows

A free-body diagram usually includes:

• the object, drawn as a box, dot, or other simple shape
• one arrow for each external force acting on that object
• labels such as weight $mg$, normal force $N$, tension $T$, friction $f$, or an applied force
• axes if they make the directions or components easier to handle

The key word is external. Weight belongs because Earth pulls on the object. A normal force belongs because a surface pushes on the object. Tension belongs because a rope pulls on the object.

How to draw a free-body diagram

For most intro physics problems, this four-step process is enough:

1. Choose one object only.
2. Replace it with a simple box or dot.
3. Add one arrow for each external force acting on that object.
4. Label each force and choose axes that make the problem easier.

That is enough to start writing equations. If a force acts at an angle, you may later split it into $x$- and $y$-components, but the first diagram should show the actual force before you break it apart.

What to leave out

Leaving things out is where many mistakes start. A free-body diagram should not include:

• velocity or acceleration drawn as if they were forces
• forces acting on some other object
• a force added only because the object is moving
• the Newton's third-law partner unless it also acts on the chosen object

For example, if a box pushes down on a table, that downward force acts on the table. It does not belong on the box's free-body diagram.

Worked example: box pulled across a rough floor

Suppose a box is pulled to the right by a horizontal rope while sliding across a rough floor. Draw the diagram for the box only, not for the rope or the floor.

The forces on the box are:

• weight $mg$ downward
• normal force $N$ upward from the floor
• tension $T$ to the right from the rope
• kinetic friction $f_k$ to the left from the floor

Once the diagram is clear, write Newton's second law for each direction:

$$\sum F_x = T - f_k$$ $$\sum F_y = N - mg$$

If the box moves at constant speed and the rope is horizontal, then the acceleration is zero. Under that condition,

$$T = f_k$$

and

$$N = mg$$

Those equalities depend on the condition. If the box speeds up, then $T > f_k$. If the rope pulls upward at an angle, then you should not assume $N = mg$ because part of the pull changes the vertical force balance.

Common free-body diagram mistakes

• Mixing up motion and force. An object can move to the right while the net force is zero.
• Forgetting to choose one object. A free-body diagram is not a picture of the whole situation.
• Assuming every contact force exists automatically. Friction, for example, appears only if the contact and motion conditions support it.
• Writing $N = mg$ by habit. That is true only in specific cases, not in every problem.

When free-body diagrams are used

Free-body diagrams show up in nearly every mechanics topic: blocks on surfaces, pulleys, inclines, equilibrium, and Newton's second law problems. They are often the step that turns a word problem into a solvable force equation.

If you want a practical next step, try your own version on a simple incline or pulley problem. Then compare your force picture with Newton's second law and Newton's third law so you do not mix up force balance with action-reaction pairs.