• Newton's?third law of motion?states:

Whenever two bodies interact, the forces they exert on each other are equal and opposite?

• Newton's third law explains the following important principles about forces:
  • All forces arise in?pairs?- if object A exerts a force on object B, then object B exerts an?equal?and?opposite?force on object A
  • Force pairs are of the?same type?- for example, if object A exerts a?gravitational?force?on object B, then object B exerts an equal and opposite?gravitational?force?on object A

   

• Newton's third law explains the forces that enable someone to walk
• The image below shows an example of a pair of equal and opposite forces acting on two objects (the ground and a foot):

The foot pushes the ground backwards, and the ground pushes the foot forwards. Newton's third law explains the forces that enable people to walk

• One force is from the foot that pushes the ground backwards
• The other is an?equal and opposite?force from the ground that pushes the foot forwards

Step 1: State Newton's first law of motion

• • Objects will remain at rest, or move with a constant velocity unless acted on by a resultant force

   

Step 2: State Newton's third law of motion

• • Whenever two bodies interact, the forces they exert on each other are equal and opposite

   

Step 3: Check if the diagram satisfies the two conditions for identifying Newton's third law

• • In each case, Newton's third law identifies pairs of equal and opposite forces, of the same type, acting on two different objects
  • The diagram only involves?one object
  • Furthermore, the forces acting on the object are different types of force - one is a?contact?force?(from the table) and the other is a?gravitational force?on the book (from the Earth) - its?weight
  • The image below shows how to apply Newton's third law correctly in this case, considering the pairs of forces acting:

   

Step 4: Conclude who is correct

• • In this case,?William is correct
  • The free-body force diagram in the question is an example of?Newton's first law?
  • The book is?at rest?because the two forces acting on it are?balanced?- i.e. there is no?resultant force

   

Newton's Third Law in Collisions

• When one object exerts a force on another object, the second object will exert an equal force on the first object in the opposite direction
• When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum)

Newton's third law can be applied to collisions

• Consider the collision between two trolleys,?A?and?B:
  • When trolley?A?exerts a force on trolley?B, trolley?B?will exert an equal force on trolley?A?in the opposite direction

   

• In this case:

F_B–A?= –F_A–B

• While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude
• From Newton's second law, acceleration depends upon both force and mass, this means:
  • For objects of equal mass, they will have equal accelerations
  • For objects of unequal mass, they will have unequal accelerations