Newton's Third Law Calculator

General Physics

This tool demonstrates Newton's third law by calculating the reaction force and the acceleration of two interacting objects.

Practical Examples

See how Newton's Third Law applies in different scenarios. Load an example to see the calculation in action.

Two Astronauts Pushing Off

Astronauts in Space

Two astronauts push off each other in a zero-gravity environment. This example calculates the resulting accelerations.

Mass A: 60 kg, Mass B: 80 kg

Force A on B: 50 N

Cannon and Cannonball

Cannon Firing

A cannon fires a cannonball. The force on the cannon (recoil) is equal and opposite to the force on the ball.

Mass A: 5 kg, Mass B: 500 kg

Force A on B: 10000 N

Leaning Against a Wall

Person and Wall

A person leans against a wall. The wall pushes back with an equal and opposite force, keeping the person upright.

Mass A: 70 kg, Mass B: 10000 kg

Force A on B: 200 N

Rocket Engine Thrust

Rocket Propulsion

A rocket expels gas downwards (action). The gas pushes the rocket upwards (reaction), creating thrust.

Mass A: 500000 kg, Mass B: 1000 kg

Force A on B: 7500000 N

Other Titles
Understanding Newton's Third Law: A Comprehensive Guide
An in-depth look at the fundamental principle of action and reaction that governs our physical world.

What is Newton's Third Law of Motion?

  • The Principle of Action and Reaction
  • Key Characteristics of Action-Reaction Pairs
  • Why It's a 'Law' of Motion
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces is equal, and their direction is opposite. This law is fundamental to understanding dynamics and how objects move and interact.
The Principle of Action and Reaction
When you push on a wall, the wall pushes back on you with a force equal in magnitude and opposite in direction. If you kick a ball, the ball also kicks you back with the same force. The 'action' is the force you exert, and the 'reaction' is the force the object exerts back on you. It's crucial to remember that these two forces act on different objects; one acts on the wall, and the other acts on you.
Key Characteristics of Action-Reaction Pairs
Action-reaction force pairs have three key features: 1) They are always equal in magnitude. 2) They are always opposite in direction. 3) They always act on different objects. This is why they don't cancel each other out. The effect of the forces (the acceleration) depends on the mass of the objects involved, as described by Newton's Second Law (F=ma).

Step-by-Step Guide to Using the Newton's Third Law Calculator

  • Inputting Your Values
  • Interpreting the Results
  • Using the 'Reset' and 'Examples' Features
Our calculator simplifies the application of Newton's Third Law to practical problems. It helps you visualize the consequences of the action-reaction principle by calculating the forces and resulting accelerations.
Inputting Your Values
1. Mass of Object A (kg): Enter the mass of the first object. 2. Mass of Object B (kg): Enter the mass of the second object. 3. Action Force (A on B) (N): Input the force that object A exerts on object B in Newtons. This is your 'action' force.
Interpreting the Results
Once you click 'Calculate', the tool provides: 1. Reaction Force (B on A): This is the force object B exerts back on object A. It will be equal in magnitude and opposite in direction to the action force. 2. Acceleration of Object A: The acceleration experienced by object A due to the reaction force. 3. Acceleration of Object B: The acceleration experienced by object B due to the action force.

Real-World Applications of Newton's Third Law

  • Rocket Propulsion and Jet Engines
  • The Act of Walking and Swimming
  • Vehicle Motion and Tire Grip
Newton's Third Law is not just a textbook concept; it's visible everywhere in our daily lives.
Rocket Propulsion and Jet Engines
A rocket works by expelling hot gas out of its engines at high velocity. This is the 'action'. In 'reaction', the gases push the rocket in the opposite direction, propelling it forward. The same principle applies to jet engines pushing air backward to move an airplane forward.
The Act of Walking and Swimming
When you walk, you push the ground backward with your feet (action). The ground pushes you forward with an equal and opposite force (reaction), which is what moves you. Similarly, a swimmer pushes water backward with their hands and feet, and the water pushes them forward.

Common Misconceptions and Correct Methods

  • Do Action-Reaction Forces Cancel Out?
  • Does the 'Action' Happen Before the 'Reaction'?
  • Force vs. Acceleration
Do Action-Reaction Forces Cancel Out?
A very common misconception is that because the forces are equal and opposite, they should cancel each other out, resulting in no motion. This is incorrect because the forces act on different objects. To determine an object's motion, you only consider the forces acting on that object. The force on object A and the force on object B are separate.
Force vs. Acceleration
While the forces in an action-reaction pair are always equal, the resulting accelerations are often not. According to Newton's Second Law (a = F/m), an object with less mass will experience a greater acceleration for the same amount of force. This is why a cannon recoils with much less acceleration than its cannonball, which has much less mass.

Mathematical Derivation and Examples

  • The Core Formula
  • Calculating Acceleration
  • Worked Example: Skaters on Ice
The Core Formula
The mathematical representation of Newton's Third Law is simple but profound: FAB = -FBA. Here, FAB is the force exerted by object A on object B, and FBA is the force exerted by object B on object A. The negative sign indicates that the forces are in opposite directions.
Calculating Acceleration
To find the acceleration of each object, we use Newton's Second Law. The acceleration of object A (aA) is caused by the force from B (FBA), so: aA = FBA / m_A. The acceleration of object B (aB) is caused by the force from A (FAB), so: aB = FAB / m_B.
Worked Example: Skaters on Ice
Imagine a 60 kg skater (A) pushing a 90 kg skater (B) with a force of 45 N. Action force FAB = 45 N. The reaction force is FBA = -45 N. Skater B's acceleration is aB = 45 N / 90 kg = 0.5 m/s². Skater A's acceleration is aA = -45 N / 60 kg = -0.75 m/s². They accelerate in opposite directions.