Free-Body Diagrams (HL IB Physics)

• Forces are pushes or pulls that occur due to the interaction between objects

• 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 multiple forces acting in different directions on multiple objects 
• To simplify these situations, free-body force diagrams can be used
• Free-body force diagrams show:
  • Multiple forces acting on one object
  • The direction of the forces
  • The magnitude of the forces

• Each force is represented as a vector arrow
  • The length of the arrow represents the magnitude of the force 
  • The direction of the arrow shows the direction in which the force acts
• Each force arrow is labelled with either:
  • a description of the type of force acting and the objects interacting with clear cause and effect
    • The gravitational pull of the Earth on the ball
  • the name of the force
    • Weight
  • an appropriate symbol
    • F_g

• Free body diagrams can be used to:
  • identify which forces act in which plane
  • determine the resultant force 

• The rules for drawing a free-body diagram are:
  • Multiple forces acting on one object
  • The object is represented as a point mass
  • Only the forces acting on the object are included
  • The forces are drawn in the correct direction
  • The forces are drawn with proportional magnitudes
  • The forces are clearly labelled

Free-body diagrams for different situations

• The most common forces to apply are:
  
  • Weight (F_g) - always towards the surface of the planet
  • Tension (F_T) - always away from the mass 
  • Normal Reaction Force (F_N) - perpendicular to a surface
  • Frictional Forces (F_f) - in the opposite direction to the motion of the mass

• Free-body diagrams can be analysed to find the resultant force acting within a system
• A resultant force is the vector sum 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 change in the object's motion: 
  • 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
• Then, the resultant force acting on the body is zero
  • For example, the weight force of a book on a desk is balanced by the normal contact 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 non-zero 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 on the rope with a force 80 N to the left and Person B pulls on the rope with a force of 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 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 all of the forces acting on the object taking into account the direction of the forces
• This is easiest to visualise when they are drawn as a free-body diagram 

• 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