Lesson 2 of 4
Pairs of forces
I can apply balanced and unbalanced forces to changes in motion, and identify interaction pairs on two bodies.Syllabus
Syllabus K223 / K224, 4(a). Apply balanced and unbalanced forces to changes in motion, and identify interaction pairs on two bodies.
Make a guess. You are not marked.
A rocket engine pushes exhaust gases out backwards. What pushes the rocket forwards?
Show the answer
The gases push forwards on the rocket, the third-law partner force.
The rocket pushes the gases backwards, so the gases push the rocket forwards with an equal force. This works in space, where there is no air.
In short
- When A pushes on B, B pushes back on A with an equal and opposite force.
- The two forces act on different objects, so they do not cancel.
- A swimmer pushes water backwards, and the water pushes the swimmer forwards.
When two bodies interact, each exerts a force on the other. The two forces have equal magnitudes and opposite directions.
A free-body diagram contains forces on one body. An interaction pair spans two bodies, so its members belong on different body diagrams.
This is Newton's third law: if body A exerts a force on body B, then B exerts a force on A that is equal in magnitude and opposite in direction.
These are often called action-reaction pairs. The forces occur together; "reaction" does not mean a later response. Identify the pair by naming both bodies and then reversing their roles.
One contact interaction, two different bodies. Only the paired contact forces are shown.
The table pushes the book upwards
Selected body: book
The book pushes the table downwards
Selected body: table
Balanced forces and interaction pairs answer different questions
| Two forces that balance on the book | A contact interaction pair |
|---|---|
| Table on book, upwards. Earth on book, downwards. | Table on book, upwards. Book on table, downwards. |
| Both act on the same body. Their resultant on that body is zero. | They act on different bodies. They belong to the same book-table interaction. |
The table's support and the book's weight can be equal and opposite, but that alone does not make them an interaction pair. One comes from contact with the table; the other comes from gravitational attraction by Earth.
The partner of Earth's gravitational force on the book is the book's gravitational force on Earth. These also have equal magnitudes and opposite directions. Earth's very large mass means its resulting acceleration from this interaction is extremely small.
Worked explanation
A hand pushing a wall
A hand pushes horizontally on a wall with a force of 12 N. The wall exerts a 12 N force on the hand in the opposite direction.
On a diagram of the hand, include the wall's force on the hand. The hand's force on the wall acts on the other body, so it does not belong on that diagram. The pair does not cancel within the hand's force diagram.
Equal forces do not require equal accelerations of the two bodies. Their masses and the other forces acting on each body matter.
Name the interaction, not just the arrow directions. "Force on the book by the table" pairs with "force on the table by the book". Swapping the bodies keeps you from confusing this pair with the book's weight.
Check your understanding
A table pushes upwards on a book resting on it. Which force is the other member of this interaction pair?
Show the answer
The book pushing downwards on the table.
This is the other force in the same book-table contact interaction. The forces have equal magnitudes and opposite directions, and act on different bodies.