MECHANICSClassical MechanicsPhysics Calculator
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Newton's Third Law

For every action there is an equal and opposite reaction. F_A on B = -F_B on A. Forces come in pairs. Explains rockets, walking, and collisions.

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Forces always come in pairs F_AB = -F_BA (same magnitude) a = F/m: smaller mass, larger a Rocket: eject mass backward โ†’ thrust forward

Key quantities
F_AB = -F_BA
Action-Reaction
Key relation
Equal magnitude
Force Pair
Key relation
a = F/m
Different a
Key relation
ฮฃp = const
Momentum
Key relation

Ready to run the numbers?

Why: Third law explains propulsion, contact forces, and why we can walk. Equal forces don't mean equal accelerationsโ€”mass matters. Fundamental to all mechanics.

How: F_action = -F_reaction. Same magnitude, opposite direction. a = F/m so different masses have different accelerations. Momentum conserved: m1v1 + m2v2 = const.

Forces always come in pairsF_AB = -F_BA (same magnitude)

Run the calculator when you are ready.

Calculate Action-ReactionEnter action force and masses
๐ŸงฑPerson Pushing WallPerson exerts 100N on wall
๐Ÿš€Rocket PropulsionGas exhaust thrust
๐ŸšถWalking MotionFoot pushes ground
๐ŸŠSwimmer Push-offPush off pool wall
๐Ÿ’ฅCollision AnalysisTwo cars collide
๐Ÿ”ซGun RecoilBullet and gun forces
๐ŸคธTrampoline JumpSpring force reaction
๐ŸšฃRowing BoatOar pushes water

Input Parameters

โ—Newton's Third Law Results
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Newton's Third Law Calculation
F_action = F_reaction = 100.00 N
Object 1: aโ‚ = 1.4286 m/sยฒ โ€ข Object 2: aโ‚‚ = 0.100000 m/sยฒ
Results Terminal
$ Action Force: 100.00 N
$ Reaction Force: 100.00 N
$ Object 1 Acceleration: 1.4286 m/sยฒ
$ Object 2 Acceleration: 0.100000 m/sยฒ

Step-by-Step Calculation

Newton's Third Law Analysis
For every action, there is an equal and opposite reaction: Fโ‚โ‚‚ = -Fโ‚‚โ‚F_action = -F_reaction
Given Values
Action Force: 100 N
Mass 1 (acting object): 70 kg
Mass 2 (reacting object): 1000 kg
Apply Third Law
Reaction force equals action force in magnitudeF_reaction = -F_action
F_reaction = -100 N = -100 N
Calculate Accelerations (F = ma โ†’ a = F/m)
Object 1 feels reaction: aโ‚ = 100.00 / 70aโ‚ = 1.4286 m/sยฒ
Object 2 feels action: aโ‚‚ = 100.00 / 1000aโ‚‚ = 0.100000 m/sยฒ
Key Insight
Forces are equal in magnitude but act on DIFFERENT objects
Larger mass experiences smaller acceleration (a = F/m)

Visualizations

For educational and informational purposes only. Verify with a qualified professional.

๐Ÿ”ฌ Physics Facts

๐ŸŽ

Action and reaction act on different bodies

โ€” HyperPhysics

โš–๏ธ

Walking: push ground back, ground pushes you forward

โ€” Physics Classroom

๐Ÿš€

Rockets: eject gas backward, gas pushes rocket forward

โ€” NASA

๐Ÿ“Š

Collision: forces equal but accelerations differ by mass ratio

โ€” Khan Academy

๐Ÿ“‹ Key Takeaways

  • โ€ข Action-reaction pairs: Forces always occur in pairs โ€” when object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A
  • โ€ข Equal magnitude, opposite direction: The forces are equal in magnitude but opposite in direction โ€” Fโ‚โ‚‚ = -Fโ‚‚โ‚
  • โ€ข Forces on different objects: Action and reaction forces act on DIFFERENT objects, so they cannot cancel each other out โ€” this is why objects can accelerate despite equal forces
  • โ€ข Simultaneous occurrence: Both forces occur at exactly the same instant โ€” there is no delay between action and reaction
  • โ€ข Momentum conservation: The Third Law implies conservation of momentum in isolated systems โ€” total momentum remains constant

๐Ÿ’ก Did You Know?

๐Ÿš€Rocket propulsion relies entirely on Newton's Third Law โ€” rockets expel exhaust gases backward, and the gases push the rocket forward with equal force. This works even in vacuum!Source: NASA
๐ŸšถWalking is possible because of the Third Law โ€” your foot pushes backward on the ground, and the ground pushes forward on your foot, propelling you forward.Source: Biomechanics
๐Ÿ“šNewton published his three laws in "Principia Mathematica" in 1687, revolutionizing physics by unifying terrestrial and celestial mechanics.Source: History of Science
๐ŸŒŒThe International Space Station uses reaction control thrusters that demonstrate the Third Law โ€” small jets expel gas to rotate and maneuver the station.Source: Space Engineering
๐Ÿ”ซGun recoil demonstrates equal forces โ€” the bullet and gun experience equal forces, but the gun's larger mass means much less acceleration (recoil).Source: Ballistics
๐ŸŠSwimming works by pushing water backward โ€” each stroke pushes water one way, and water pushes the swimmer forward with equal force.Source: Fluid Dynamics

๐Ÿ”ฌ How It Works

Newton's Third Law: Fโ‚โ‚‚ = -Fโ‚‚โ‚

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means forces always occur in pairs. When object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A. The key insight is that these forces act on DIFFERENT objects, which is why they don't cancel out.

Equal Magnitude

Both forces have exactly the same magnitude. If you push a wall with 100 N, the wall pushes back with 100 N โ€” not 99 N or 101 N.

Opposite Direction

The forces point in exactly opposite directions. If one force points north, the other points south โ€” 180ยฐ apart.

Different Objects

Action acts on object B, reaction acts on object A. Since they act on different objects, they cannot cancel โ€” both objects can accelerate.

Simultaneous

Both forces occur at the exact same instant. There is no delay โ€” "action" and "reaction" are just names, neither causes the other.

๐Ÿ’ผ Expert Tips

Problem Solving

Identify force pairs correctly: True action-reaction pairs always involve the SAME two objects. Weight (Earth-object) and normal force (floor-object) are NOT a pair โ€” they involve different object pairs.

Common Mistake

Remember forces don't cancel: Action and reaction forces act on different objects, so they cannot cancel. Only forces acting on the SAME object can cancel. This is why objects accelerate despite equal forces.

Calculation

Use F = ma for each object separately: Calculate acceleration for each object using F = ma, where F is the net force ON that object. Larger mass means smaller acceleration for the same force magnitude.

Advanced

Apply momentum conservation: In isolated systems, the Third Law implies momentum conservation: mโ‚vโ‚ + mโ‚‚vโ‚‚ = constant. Use this to solve collision and recoil problems.

๐Ÿ“Š Comparison: Newton's Three Laws

LawStatementFormulaKey Concept
First (Inertia)Object at rest stays at rest; object in motion stays in motion unless acted on by net forceฮฃF = 0 โ†’ v = constInertia
Second (F=ma)Acceleration is proportional to net force and inversely proportional to massF = maForce causes acceleration
Third (Action-Reaction)Every action has an equal and opposite reactionFโ‚โ‚‚ = -Fโ‚‚โ‚Forces come in pairs

โ“ Frequently Asked Questions

If forces are equal, why don't they cancel out?

Action and reaction forces act on DIFFERENT objects, so they can't cancel. Forces only cancel when acting on the SAME object. When you push a wall, you feel the wall push back on you โ€” but the wall's reaction acts on you, not itself.

Why does only one object move sometimes?

Both objects ALWAYS experience equal forces, but acceleration depends on mass (a = F/m). When you push a car, both you and the car feel equal forces, but the car barely accelerates due to its huge mass, while you might slide backward.

How do rockets work in vacuum (space)?

Rockets don't push against air! They work by the Third Law: the rocket pushes exhaust gases backward, and the gases push the rocket forward. This works perfectly in vacuum โ€” in fact, it works BETTER without air resistance.

Is there a delay between action and reaction?

No! Action and reaction forces occur simultaneously โ€” at the exact same instant. There is no cause-and-effect delay. The naming "action" and "reaction" is somewhat misleading; they're really just "interaction pairs."

Why do larger objects exert more force?

They don't! Both objects exert EQUAL forces. The larger object just accelerates less (a = F/m). A small bullet and large gun experience equal forces during firing, but the gun's huge mass means minimal recoil acceleration.

Can action-reaction pairs be different types of forces?

No. Action-reaction pairs are always the SAME type of force. If the action is a contact force, the reaction is also a contact force. If the action is gravitational, the reaction is also gravitational.

How does the Third Law relate to momentum conservation?

The Third Law implies momentum conservation. When two objects interact, their forces are equal and opposite, so the total force on the system is zero. This means total momentum (pโ‚ + pโ‚‚) remains constant in isolated systems.

What happens if one object is much more massive?

Both objects still experience equal forces, but the more massive object accelerates much less. For example, Earth pulls you down with your weight, and you pull Earth up with equal force โ€” but Earth barely moves because its mass is enormous.

๐Ÿ“Š Newton's Third Law by the Numbers

Fโ‚โ‚‚ = -Fโ‚‚โ‚
Core Formula
Equal
Force Magnitude
180ยฐ
Opposite Direction
1687
Published Year

โš ๏ธ Disclaimer

This calculator is for educational purposes. Results are approximations based on ideal conditions. Real-world applications may involve friction, air resistance, and other factors not accounted for here. For engineering applications, consult appropriate design standards and safety factors.

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