Newton's Third Law said forces come in pairs. With Free-Body Diagrams we can say exactly which forces pair up, and it is not always the pair you expect.
Key idea
If A exerts a force on B, then B exerts a force on A that is equal in size, opposite in direction and of the same type. The two forces act on different objects, so they never appear on the same free-body diagram.
Why it works
A force is an interaction between two objects, and an interaction has two ends. When your hand pushes a wall, the wall pushes your hand: one interaction, seen from each side. Because the forces act on different objects, they can't cancel each other; each changes the motion of its own object according to that object's mass.
Worked examples
Worked example: Finding the partner
Earth pulls a book down with gravity. What is the third-law partner of that force?
- Swap the objects: the book pulls Earth.
- Same type (gravity), same size, opposite direction: the book pulls Earth up.
- The table's upward push on the book is not the partner: it acts on the same object (the book) and is a different type (a contact force).
Answer: The book's gravitational pull on Earth, upward
Worked example: Unequal masses
A $2{,}000\ \text{kg}$ truck bumps a $1{,}000\ \text{kg}$ car, pushing it with $8{,}000\ \text{N}$. Find each one's acceleration.
- Third law: the car pushes the truck with $8{,}000\ \text{N}$ too.
- Car: $\dfrac{8000}{1000} = 8\ \text{m/s}^2$. Truck: $\dfrac{8000}{2000} = 4\ \text{m/s}^2$.
- Equal forces, unequal effects: the lighter car gets the bigger acceleration.
Answer: Car $8\ \text{m/s}^2$; truck $4\ \text{m/s}^2$
Common mistake
Calling weight and the normal force a third-law pair (they act on the same object, and they aren't always equal, as in an elevator), or thinking the heavier or faster object pushes harder. Check a proposed pair with three questions: different objects? same type of force? the description reads the same with the two objects swapped?
Try it in the Science Lab: The Third Law: Action and Reaction.