Free-Body Diagrams & Newton’s Third Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
A free-body diagram shows only the forces exerted on one object. Newton’s third law says forces come in pairs: if A pushes on B, B pushes back on A just as hard. Those two forces act on different objects, so they never cancel each other.
1. Drawing a free-body diagram
1. Pick one object and draw it as a dot.
2. Add gravity (Earth on the object), then one force for each thing touching it: floor, rope, hand, wall.
3. Draw each force as an arrow starting at the dot, pointing the way that force pushes or pulls.
4. Label each arrow with who exerts it on whom: “force of the floor on the box.”
2. Newton’s third law: forces come in pairs
The two forces in a pair are always equal in size, opposite in direction, and the same type of force.
To find a partner, swap the names: the partner of “floor on box” is “box on floor.”
Weight and the normal force are not a pair. Both act on the box. When they are equal, that’s because the box isn’t accelerating vertically, not because of the third law.
3. Example, then try it
A student pushes on a wall with 40 N. What force does the wall exert on the student?
The pair is “student on wall” and “wall on student,” so the wall pushes back with 40 N, pointing away from the wall.
That push from the wall is what moves the student backward if she’s on skates.
A book rests on a table. Name the third-law partner of (a) the table’s normal force on the book and (b) Earth’s gravitational force on the book. Are the book’s weight and the normal force a third-law pair?
(a) Swap the names: the book’s push down on the table.
(b) Swap the names: the book’s gravitational pull up on Earth.
Weight and normal force both act on the book, so they can’t be a pair. They are equal here only because the book isn’t accelerating.
Answer: (a) book on table, (b) book on Earth. Weight and normal force are not a third-law pair.
4. Common mistakes
A truck collides with a small car. During the collision, how does the force of the truck on the car compare with the force of the car on the truck?
They are a third-law pair, so they are always equal in size and opposite in direction. The car feels a much bigger acceleration because its mass is smaller.
Ready to practice?
4 questions on Free-Body Diagrams & Newton’s Third Law, each with a hint and an explanation for every wrong answer.