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Newton's Third Law Calculator

Explore reaction forces and law of motion

Interaction Parameters

This tool demonstrates Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. [1, 2] When two objects interact, the force exerted by the first object on the second is equal in magnitude and opposite in direction to the force exerted by the second on the first. [3]

  • Action-Reaction Pair: The forces are always equal, but the resulting accelerations depend on the mass of each object (from F=ma). [4]
  • Consequences: A small object will experience a much greater acceleration than a large object when the same force is applied to both. This is why a person on roller skates moves backward when pushing against a wall. [5]

F12 = -F21

a = F/m

Enter parameters and click Calculate

About Newton's Third Law Calculator

About Newton's Third Law Calculator

Understanding action-reaction force pairs and their fundamental role in physics

⚡ What is Newton's Third Law?

Newton's Third Law of Motion is a fundamental principle that describes how forces always occur in pairs. It states that for every action, there is an equal and opposite reaction.

The Mathematical Statement

F₁₂ = -F₂₁

Where F₁₂ is the force of object 1 on object 2, and F₂₁ is the force of object 2 on object 1

This law tells us that when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. These forces are always equal in magnitude, opposite in direction, and act on different objects simultaneously.

🔑 Key Concepts

Action-Reaction Pairs

Forces never exist in isolation. Every force has a corresponding reaction force that is equal in magnitude but opposite in direction.

Example: When you push a wall, the wall pushes back on you with equal force.

Different Objects

The action and reaction forces act on different objects, not the same object. This is why objects can accelerate even though forces are equal and opposite.

Important: Action force acts on object B, reaction force acts on object A.

Simultaneous Forces

Both forces in an action-reaction pair occur at exactly the same time. There's no delay between the action and the reaction.

Timing: The forces are instantaneous and simultaneous.

System Perspective

When considering the entire system (both objects), the net force is zero. However, individual objects within the system can still accelerate.

Net Force: F_net = F₁₂ + F₂₁ = F₁₂ + (-F₁₂) = 0

⚠️ Common Misconceptions

❌ Forces Cancel Out

Many people think action and reaction forces cancel each other out, preventing motion. This is incorrect because the forces act on different objects.

✅ Individual Acceleration

Each object can accelerate independently because the forces act on different objects. The net force on the system is zero, but individual objects can move.

❌ Cause and Effect

People often think one force causes the other. In reality, both forces occur simultaneously - neither is the cause of the other.

✅ Simultaneous Forces

Both forces exist at the same instant. When you push on something, it pushes back immediately. There's no time delay between action and reaction.

🚀 Real-World Applications

🚀 Rocket Propulsion

Rocket engines expel gas backward, and the gas pushes the rocket forward with equal force.

🏃 Walking and Running

Your foot pushes backward on the ground, and the ground pushes forward on your foot.

🚗 Car Motion

Car wheels push backward on the road, and the road pushes forward on the car.

🎾 Ball Sports

When a ball hits a surface, the surface exerts an equal and opposite force on the ball.

🌊 Swimming

Swimmers push water backward, and water pushes swimmers forward.

🪂 Parachuting

Air resistance pushes up on the parachute, and the parachute pushes down on the air.

🛠️ Calculator Features

Force Analysis

  • Action Force Input: Set the magnitude of the action force
  • Automatic Reaction: Calculator shows equal and opposite reaction force
  • System Analysis: Shows net force on the entire system
  • Visual Comparison: Charts display action-reaction relationships

Motion Analysis

  • Mass Parameters: Input masses of both objects
  • Displacement Tracking: Shows how objects move over time
  • Collision Analysis: Analyzes momentum in collisions
  • Real-time Updates: Results update as you change inputs

💡 Examples and Demonstrations

Person Pushing Wall

When you push a wall with 100N, the wall pushes back with 100N. You don't move the wall because it's attached to the ground, but you can feel the reaction force.

Rocket Launch

A rocket engine exerts 1,000,000N on the exhaust gases, and the gases exert 1,000,000N back on the rocket, propelling it upward.

Ball Bouncing

When a ball hits the ground with 50N force, the ground exerts 50N back on the ball, causing it to bounce back up.

💡 Tips for Understanding

Visualize the Forces

  • Draw force diagrams for both objects
  • Use arrows to show force directions
  • Remember forces act on different objects
  • Consider the system as a whole

Practical Applications

  • Observe everyday interactions
  • Notice how you move through the world
  • Think about sports and motion
  • Consider transportation systems

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. When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Mathematically, this is expressed as F₁₂ = -F₂₁, where F₁₂ is the force of object 1 on object 2, and F₂₁ is the force of object 2 on object 1.
How do I use this calculator?
Enter the action force magnitude, set the masses of both objects, and choose your analysis type (force analysis, motion analysis, or collision analysis). The calculator will automatically show the reaction force, net force on the system, and generate relevant charts. You can also click on common examples to see typical force values.
Why don't action and reaction forces cancel each other out?
Action and reaction forces act on different objects, not the same object. While the net force on the entire system is zero, individual objects can still accelerate because each force acts on a different object. For example, when you push a wall, the wall pushes back on you, but you can still move away from the wall.
What units should I use?
Use SI units: force in newtons (N) and mass in kilograms (kg). The calculator will automatically handle the calculations and display results in these units. For example, a 50N force pushing on a 10kg object.
Can objects move even when forces are equal and opposite?
Yes! Objects can move even when action and reaction forces are equal and opposite because these forces act on different objects. Each object experiences only one of the forces, so they can accelerate independently. The net force on the system is zero, but individual objects can still move.
What's the difference between this law and the other Newton's laws?
Newton's First Law deals with objects at rest or in uniform motion (inertia). Newton's Second Law relates force, mass, and acceleration (F = ma). Newton's Third Law describes how forces always occur in pairs - for every action force, there's an equal and opposite reaction force acting on a different object.
How is this law used in rocket propulsion?
In rocket propulsion, the rocket engine exerts a force on the exhaust gases, pushing them backward. According to Newton's Third Law, the gases exert an equal and opposite force on the rocket, pushing it forward. This is how rockets can move in space where there's nothing to push against.
What happens in a collision between two objects?
In a collision, each object exerts a force on the other. Object A pushes on Object B, and Object B pushes back on Object A with equal and opposite force. The momentum of the system is conserved, but individual objects can change their motion due to these action-reaction forces.
Why do I feel a force when I push against a wall?
When you push against a wall, you exert a force on the wall. According to Newton's Third Law, the wall exerts an equal and opposite force back on you. You can feel this reaction force because it's pushing on your hand/body, even though the wall itself doesn't move (because it's attached to the ground).
How does this law apply to walking?
When you walk, your foot pushes backward against the ground. The ground exerts an equal and opposite force forward on your foot, which propels you forward. This is why you can walk on solid ground but not on ice (where there's less friction to provide the reaction force).
What's the significance of the net force being zero?
The net force on the entire system (both objects) is zero because the action and reaction forces cancel each other out. This means the total momentum of the system is conserved. However, individual objects can still accelerate because each experiences only one of the forces in the pair.
Can this law be violated?
No, Newton's Third Law is a fundamental law of physics that has never been observed to be violated. It applies to all types of forces - gravitational, electromagnetic, nuclear, and contact forces. Any apparent violation usually indicates that we haven't identified all the forces in the system.
How do I interpret the charts in the calculator?
The Action-Reaction Forces chart shows how action and reaction forces are always equal in magnitude but opposite in direction. The Motion Analysis chart shows how two objects move over time when subjected to action-reaction forces. The Collision Analysis chart shows momentum relationships in collisions.
What are some real-world examples of this law?
Common examples include: rocket propulsion (rocket pushes gas, gas pushes rocket), walking (foot pushes ground, ground pushes foot), swimming (arms push water, water pushes swimmer), ball bouncing (ball pushes surface, surface pushes ball), and car motion (wheels push road, road pushes car).
How does this law relate to conservation of momentum?
Newton's Third Law is directly related to conservation of momentum. When two objects interact, the action-reaction forces ensure that the total momentum of the system remains constant. If object A gains momentum in one direction, object B gains equal momentum in the opposite direction, keeping the total momentum unchanged.

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