Free-body Force Diagrams
- Free body diagrams are useful for modeling the forces that are acting on an object
- Each force is represented as a vector arrow, where each arrow:
- Is scaled to the magnitude of the force it represents
- Points in the direction that the force acts
- Is labelled with the name of the force it represents or an appropriate symbol
- Free body diagrams can be used:
- To identify which forces act in which plane
- To resolve the net force in a particular direction
Simple Free Body Diagrams
- The rules for drawing a free-body diagram are the following:
- Rule 1: Draw a point in the centre of mass of the body
- Rule 2: Draw the body free from contact with any other object
- Rule 3: Draw the forces acting on that body using vectors with correct direction and proportional length
Free body diagrams can be used to show the various forces acting on objects
Forces on a Particle or an Extended but Rigid Body
- Free body diagrams simplify problems by reducing complex shapes into simple one
- Any object can be thought of as a particle
- Even something as large as the Earth can be modelled as a point mass for most calculations
- Objects can also be thought of as being extended but rigid bodies
- This simply means that all parts stay in the same position relative to each other when the object moves
Point particle representation of the forces acting on a moving object
- The below example shows an object sitting on a slope in equilibrium
Three forces on an object in equilibrium form a closed vector triangle
Worked Example
Draw free-body diagrams for the following scenarios:
a) A picture frame hanging from a nail
b) A box sliding down a slope
Part (a)
A picture frame hanging from a nail:
- The size of the arrows should be such that the 3 forces would make a closed triangle as they are balanced
Part (b)
A box sliding down a slope:
- There are three forces acting on the box:
- The normal contact force, R, acts perpendicular to the slope
- Friction, F, acts parallel to the slope and in the opposite direction to the direction of motion
- Weight, W, acts down towards the Earth
- There are three forces acting on the box:
Exam Tip
When labeling force vectors, it is important to use conventional and appropriate naming or symbols such as:
- w or Weight force or mg
- N or R for normal reaction force (depending on your local context either of these could be acceptable)
Getting used to this notation will make labelling free-body diagrams automatic - leaving you time to focus on the Physics rather than the process. This is crucial as a good diagram will show you exactly what to include in your calculations.
