Free-Body Diagrams (SL IB Physics)

• Forces are created from the interaction between bodies
  • For example, a push or pull

• In physics, during force interactions, it is common to represent situations as simply as possible without losing information
  • When considering force interactions, objects are represented as point particles
  • These point particles should be placed at the centre of mass of the object

• Forces are represented by arrows because forces are vectors
  • The length of the arrow gives the magnitude of the force, and its direction gives the force's direction

• The below example shows the forces acting on an object when pushed to the right over a rough surface

Point particle representation of the forces acting on a moving object

• The below example shows the forces acting on an object suspended from a stationary rope

Forces on an object suspended from a stationary rope

Free-body Diagrams

• As situations become more complex, there are often forces on multiple objects in different directions
• Forces acting on a body can be represented by a free-body diagram
  
• 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

• The rules for drawing a free-body diagram are the following:
  • The diagram is for one object at a time
  • The body is represented by a point (the centre of mass) or a box or circle where all the forces act on
  • Only the forces acting on the body are drawn 
  • The forces must be in the correct direction and a proportional length
  • All forces must be clearly labelled

Free-body diagrams for different situations

• The most common forces to apply are:
  
  • Weight (W) - always towards the surface of the planet
  • Tension (T) - always away from the mass 
  • Normal Reaction Force (N) - upwards from a surface
  • Upthrust (U) - upwards if the mass is in a fluid (gas or liquid)
  • Frictional Forces (F_r) - in the opposite direction to the motion of the mass

• Free-body diagrams can be analysed to find the resultant force on a system
• A resultant force is a single force that describes all of the forces operating on a body
  • When many forces are applied to an object they can be combined
  • This produces one overall force which describes the combined action of all of the forces

• This single resultant force determines: 
  • The direction in which the object will move as a result of all of the forces
  • The magnitude of the total force experienced by the object

• The resultant force is sometimes called the net force
• Forces can combine to produce
  • Balanced forces
  • Unbalanced forces

• Balanced forces mean that the forces have combined in such a way that they cancel each other out and no resultant force acts on the body
  • For example, the weight of a book on a desk is balanced by the normal force of the desk
  • As a result, no resultant force is experienced by the book; the forces acting on the book and the table are equal and balanced

A book resting on a table is an example of balanced forces

• Unbalanced forces mean that the forces have combined in such a way that they do not cancel out completely and there is a resultant force on the object
  • For example, two people play a game of tug-of-war, working against each other on opposite sides of the rope
  • If person A pulls with 80 N to the left and person B pulls with 100 N to the right, these forces do not cancel each other out completely
  • Since person B pulled with more force than person A the forces will be unbalanced and the rope will experience a resultant force of (100 – 80 =) 20 N to the right

A tug-of-war is an example of when forces can become unbalanced

Resultant forces in one-dimension

• The resultant force in a one-dimensional situation i.e. when the forces are directed along the same plane, can be found by combining vectors
• Combining force vectors involves adding or subtracting all of the forces acting on the object
• This is easiest to visualise when they are drawn as a free-body diagram 
  • Forces working in opposite directions are subtracted from each other
  • Forces working in the same direction are added together

• If the forces acting in opposite directions are equal in size, then there will be no resultant force – the forces are said to be balanced

Diagram showing the resultant forces on three different objects

• Imagine the forces on the boxes as two people pushing and pulling on either side
  • In the first scenario, the two people are evenly matched - the box doesn't move
  • In the second scenario, the two people are pushing on the same side of the box, it moves to the right with their combined strength
  • In the third scenario, the two people are pushing against each other and are not evenly matched, so there is a resultant force to the left

Resultant forces in two-dimensions

• The resultant force in a two-dimensional situation i.e. when the forces are not on the same plane, can be found from resolving vectors
• Resolving force vectors involves using Pythagoras or trigonometry to determine the resultant of all of the forces acting on the object

The resultant force is easier to visualise using a free-body diagram

• For example, the two 10 N forces acting on the cardboard box produce a resultant force of
  • 

• More on these calculations can be found in Combining & Resolving Vectors