Newton's 3rd law
Brook Edgar & Hannah Shuter
Teachers
Explainer Video
Newton's Third Law
Newton's Third Law states: Whenever two objects interact, the forces they exert on each other are equal in magnitude but opposite in direction.
This is sometimes worded as: "For every action, there is an equal and opposite reaction." But be careful with this phrasing, as it makes it sound like one force causes the other, when actually both forces exist simultaneously as a result of the interaction between two objects.
Newton's Third Law pair
The two objects are known as a Newton's Third Law pair. The forces must be:
equal in magnitude (same size in newtons)
opposite in direction
the same type of force (both gravity, both friction, both normal contact, etc.)
act on different objects (this is crucial - if both forces act on the same object, they're NOT a Newton's Third Law pair)
To summarise -> If object A exerts a force on object B, then object B exerts an equal but opposite force on object A.
A Newton's law pair above is the Earth and the Sun. The Sun exerts a force on the Earth, and the Earth exerts an equal but opposite force on the Sun. This force is gravity, the non-contact force that acts between objects with mass.
But why don't the objects move equally?
If Newton's Third Law pairs are always equal, why does the Earth orbit the Sun, but the Sun barely moves? Why does a cannonball fly off but the cannon only recoils slightly?
The answer comes from Newton's Second Law, . The forces are equal in magnitude, but because the masses differ greatly, the objects experience different accelerations.
For the cannonball: . Small mass, so large acceleration
For the cannon: . Large mass, so small acceleration
Applications of Newton's Third Law
Swimming: You push water backwards, water pushes you forwards, this is how you move through water.
Walking: Your foot pushes the ground backwards, the ground pushes your foot forwards, that's how you walk forward.
Rocket propulsion: Rocket pushes hot gases down and backwards, gases push rocket up and forwards, this is how rockets work in space.
Remember: The forces are equal in magnitude under Newton's third law, but this does not mean the forces are balanced! The forces act on different objects. To see if forces are balanced to apply Newton's second law, , we need to look at the forces acting on just one object!
Worked Example:
The diagram shows a falling apple.
Label the missing force.
Is this missing force a contact or non-contact force?
Explain why the two forces are not Newton's third law pairs.
State a Newton's third law pair.
Answer:
A falling apple has two forces acting on it:
Weight (gravitational pull from Earth): Acts downwards on the apple -> already labelled.
Air resistance: Acts upwards on the apple -> but is smaller in magnitude as the apple is falling at an increasing speed.
Air resistance is a contact force; the air particles collide with the surface of the apple, and all of the tiny forces from every air particle hitting the falling apple add up to produce the upwards force of air resistance.
These are NOT Newton's Third Law pairs because:
They're different types of forces (gravity vs air resistance). Newton's third law states that the forces must be of the same type.
They both act on the same object (the apple). Newton's third law states that the forces must act on different objects.
The Newton's Third Law pairs are:
Earth pulls the apple down due to gravity, and the apple pulls the Earth up due to gravity, with an equal but opposite force.
Air pushes the apple up; the apple pushes the air particles down with an equal but opposite force.
Practice Questions
A student exerts a force of on a trolley, pushing the trolley forwards.
Complete the sentence: The trolley exerts ___ of force back on the student.
Explain why the trolley accelerates forward.
-> Check out Brook's video explanation for more help.
Answer:
The trolley exerts of force back on the student.
The action–reaction forces act on different objects. The forward force from the student on the trolley is unbalanced on the trolley, so it accelerates.
A rocket engine expels hot gases downward at high speed. The gases exert a downward force of on the surrounding air.
Complete the sentence: The air exerts an upward force of ___ on the gases.
The weight of the rocket at launch is . Determine the resultant force on the rocket and describe its motion.
-> Check out Brook's video explanation for more help.
Answer:
The air exerts an upward force of on the gases.
Resultant force upward. The rocket accelerates upward because of the unbalanced upward force.