Free Body Diagrams

Purpose of Free Body Diagrams

Free body diagrams are simple drawings used to represent all the forces acting on a single object. They help to:

• Visualise and simplify the analysis of forces
• Identify every force acting on the object clearly
• Understand how forces interact and affect motion

By focusing only on the object and the forces acting on it, free body diagrams make it easier to calculate resultant forces and predict motion.

Components of Free Body Diagrams

A free body diagram consists of:

• Object representation: The object is shown as a simple dot or a box to keep the diagram clear and uncluttered.
• Force arrows: Each force acting on the object is drawn as an arrow starting from the dot or box.
• Arrow length: The length of each arrow is proportional to the magnitude (size) of the force it represents.
• Arrow direction: The arrow points in the direction in which the force acts.

For example, if a book is resting on a table, the free body diagram would show the weight force acting downwards and the normal reaction force from the table acting upwards.

For instance, if a box is pulled to the right with a force of 10 N and friction acts to the left with a force of 4 N, the free body diagram would have a longer arrow pointing right (10 N) and a shorter arrow pointing left (4 N).

Types of Forces Included

Free body diagrams include all forces acting on the object, which can be:

• Contact forces: Forces that require physical contact between objects, such as friction, tension (pulling force in a rope), and normal reaction force (support force from a surface).
• Non-contact forces: Forces that act at a distance without physical contact, such as gravitational force (weight).
• Normal reaction force: The support force exerted by a surface perpendicular to the object resting on it.

It is important to include all relevant forces to correctly analyse the situation.

Using Free Body Diagrams

Free body diagrams are used to:

• Determine the resultant force: By adding all the forces as vectors, you can find the overall force acting on the object.
• Analyse balanced and unbalanced forces: If forces balance (resultant force is zero), the object remains stationary or moves at constant velocity. If unbalanced, the object accelerates.
• Apply Newton’s laws: Newton’s First Law (inertia) and Second Law ($F = ma$) can be applied once forces are identified.

For example, if a car is stationary on a flat road, the weight force downwards is balanced by the normal reaction force upwards, so the resultant force is zero.

If the car accelerates forward, the driving force is greater than the frictional force opposing it, resulting in an unbalanced force and acceleration.

Example: A box of mass 5 kg is pulled across a floor by a rope with a force of 20 N to the right. The frictional force opposing the motion is 8 N to the left. Draw a free body diagram and find the resultant force.

The box is represented by a dot. Two arrows are drawn: one to the right labelled 20 N (pulling force), one to the left labelled 8 N (friction). The resultant force is:

$$F_{\text{resultant}} = 20\,\text{N} - 8\,\text{N} = 12\,\text{N} \text{ (to the right)}$$

This unbalanced force means the box will accelerate to the right.