In mechanics, understanding the motion of objects is essential, and one tool that helps solve this problem is the free-body diagram. It is a simple but powerful graphical representation that succinctly represents all the forces acting on an object. A free-body diagram can represent a stationary or moving object, and is used in mechanics to explain the cause of an object's motion.

A free-body diagram transforms a complex problem into a simple representation, making it easy to understand the essential forces acting on an object, leading to a mathematical equation. In many cases, the equation would be extremely complex to derive without using free-body diagrams. To make a free-body diagram, start by selecting the object or system under inspection, isolating it from its surroundings, and drawing it as a dot or a simple outline. Next, represent all the essential external forces acting on the object or system of interest with arrows. The direction of the arrows represents the direction of the force, while the length of the arrows depicts the magnitude of the force. It is important to note that in a free-body diagram, velocity and acceleration are not represented, but can be inferred from the forces applied on the object.

Some common types of forces that can be represented in a free-body diagram include weight, normal force, tension, friction, and applied force. Weight refers to the force of gravity acting on the object, typically represented by an arrow pointing downward. Normal force is the force between two objects when they come in contact with each other; this force acts in the opposite direction to the weight of the object. Tension is generally represented by an arrow pointing away from the object in the direction of the force, and friction is the force that resists sliding between surfaces. Finally, applied force refers to the force applied to the object by an external agent, such as a push or a pull. Applied forces are represented by an arrow pointing in the direction of the force.

Consider a stationary trolley, on which two cardboard boxes are stacked. The two systems of interest, box one and box two, can be assumed to be isolated systems and can be represented using a free-body diagram. The forces acting on box one are gravitational force, which defines its weight, and the counter-balancing normal force due to box two. Similarly, the forces on box two are its weight, the normal force due to the trolley, and the weight of box one.