Interactive physics simulator
Newton's Third Law of Motion: Action & Reaction
Newton's Third Law explains that forces always come in pairs. When you push an object, it pushes back on you with the exact same amount of force in the opposite direction.
Newton's Third Law Simulator
Observe that forces are always equal and opposite, even when masses differ.
Live Telemetry
- Action Force
- 0 N
- Reaction Force
- 0 N
- Astronaut 1 Speed
- 0 m/s
- Astronaut 2 Speed
- 0 m/s
- Mass Ratio (m₁:m₂)
- 1 : 1
- Law Check
- F₁₂ = -F₂₁
What is Newton's Third Law of Motion?
Newton's Third Law of Motion states that forces always exist in pairs. When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
Commonly stated as "for every action, there is an equal and opposite reaction," this law implies that it is impossible to touch something without it touching you back with the exact same force.
Key Definition
Newton's Third Law governs interaction forces between two bodies.
- Forces always occur in action-reaction pairs.
- The action and reaction forces are exactly equal in magnitude.
- They point in exactly opposite directions.
- They act on different bodies (which is why they don't cancel).
- They occur simultaneously with zero time delay.
Third Law Formula
FAB = -FBA
- FAB = Force exerted by A on B
- FBA = Force exerted by B on A
- The minus sign (-) indicates opposite direction.
Action vs. Reaction
| Scenario | Action Force | Reaction Force |
|---|---|---|
| Walking | Feet push ground back | Ground pushes feet forward |
| Swimming | Hands push water back | Water pushes swimmer forward |
| Rocket flight | Engine ejects gas down | Gas pushes rocket up |
Real-life Recoil
When you jump off a small boat, you push the boat backward (action). The boat pushes you forward (reaction). Because the boat is free to float, it moves backward as you leap forward.
- Action: Push boat back.
- Reaction: Boat pushes you forward.
- Result: Both separate.
Solved Examples
A 70 kg astronaut floats in space and pushes a 10 kg toolbox with a force of 35 N. What is the reaction force on the astronaut, and what are their respective accelerations?
- According to Newton's Third Law, the toolbox exerts an equal and opposite force on the astronaut.
- Reaction Force = 35 N in the opposite direction.
- Astronaut's acceleration: a₁ = F / m₁ = 35 / 70 = 0.5 m/s².
- Toolbox's acceleration: a₂ = F / m₂ = 35 / 10 = 3.5 m/s².
Answer: 35 N | a₁ = 0.5 m/s², a₂ = 3.5 m/s²
A heavy truck (mass 3000 kg) collides head-on with a small car (mass 1000 kg). The truck exerts a force of 15,000 N on the car. What force does the car exert on the truck?
- By Newton's Third Law, the force of the car on the truck is equal and opposite to the force of the truck on the car.
- The car exerts exactly 15,000 N on the truck in the opposite direction.
- Note: The car will experience a larger acceleration due to its smaller mass, which is why it receives more visible damage.
Answer: 15,000 N
A book weighs 10 N and rests on a table. Identify the action-reaction pairs.
- Pair 1 (Gravity): The Earth pulls the book down with 10 N (Action). The book pulls the Earth up with 10 N (Reaction).
- Pair 2 (Contact): The book pushes the table down with 10 N (Action). The table pushes the book up with 10 N (Reaction).
Answer: Book-Earth pair (10 N) and Book-Table pair (10 N)
Common Mistakes
- Thinking forces cancel out because they are equal and opposite (they act on different bodies, so they don't cancel).
- Believing reaction happens after action (they happen simultaneously).
- Assuming heavier objects feel smaller forces in collisions (forces are equal; accelerations differ).
- Confusing action-reaction pairs with equilibrium forces.
Quick Summary
- Forces come in equal and opposite pairs.
- FAB = -FBA
- Forces act on different objects.
- Equal forces cause different accelerations if masses are unequal.
- Recoil and collisions demonstrate the law.
Practice Questions
1. If a horse pulls a carriage, the carriage pulls back on the horse with an equal force. Why does the carriage move?
The horse moves because the ground pushes the horse forward (reaction to the horse pushing the ground). The net force on the carriage is forward because the horse's pull is larger than the friction on the carriage wheels.
2. An apple falls from a tree. If the Earth pulls the apple down, does the apple pull the Earth up?
Yes, the apple pulls the Earth up with an equal force. However, because the Earth's mass is so huge, its acceleration is completely imperceptible.
3. Identify the action and reaction forces when a swimmer turns off a wall.
Action: The swimmer pushes the wall backward with their feet. Reaction: The wall pushes the swimmer forward with an equal force.
4. Why do action-reaction pairs not cancel each other out?
Action-reaction forces never cancel out because they act on different objects. Normal net force cancelation only occurs when forces act on the same object.
5. A rocket launches into space. What is the reaction force?
Action: The rocket engine ejects gas exhaust downward. Reaction: The exhaust gas pushes the rocket body upward with an equal force.
FAQ
Frequently Asked Questions
What is Newton's Third Law of Motion?
Newton's Third Law states that for every action, there is an equal and opposite reaction. Forces always occur in pairs.
What is the formula for Newton's Third Law?
The formula is F_AB = -F_BA, which means the force exerted by Object A on Object B is equal in magnitude and opposite in direction to the force exerted by Object B on Object A.
Do action and reaction forces act on the same object?
No. They always act on two different objects, which is why they do not cancel out.
Why do action-reaction forces not cancel each other out?
For forces to cancel, they must act on the same object (like two people pushing a box from opposite sides). Since action-reaction forces act on different bodies, they accelerate each body independently.
How does a balloon rocket show the Third Law?
When gas escapes from the balloon nozzle (action), the escaping gas pushes the balloon forward (reaction).
What is the reaction force to the weight of a book?
The reaction to the Earth pulling down on the book (gravity) is the book pulling up on the Earth. The normal force from the table is the reaction to the book pushing down on the table.
In a car crash, does the larger car exert a larger force?
No. Both cars exert the exact same force on each other during the collision. The smaller car accelerates more violently due to its smaller mass.
Is there a time delay between action and reaction?
No. Action and reaction forces occur simultaneously; there is no lag between them.
Why can two equal forces cause different accelerations?
Newton's Third Law says the forces are equal in magnitude, but Newton's Second Law says acceleration depends on mass. The object with smaller mass accelerates more.
How does walking show Newton's Third Law?
Your foot pushes the ground backward, and the ground pushes your foot forward with an equal and opposite force. That forward ground force moves you ahead.
How does a rocket move in space using Newton's Third Law?
A rocket pushes exhaust gases backward. The exhaust gases push the rocket forward with an equal and opposite force, even in space where there is no air to push against.
Are action and reaction forces the same type of force?
Yes. The action and reaction forces are the same interaction type, such as two contact forces, two gravitational forces, or two electric forces.