Newton's Laws Simulator — F=ma, Inertia, and Action-Reaction

Newton's Three Laws

First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force.

Second Law (F = ma): The net force on an object equals its mass times its acceleration: F_net = m × a. The direction of acceleration matches the net force direction.

Third Law (Action-Reaction): For every action force, there is an equal and opposite reaction force — acting on a different object.

Friction Coefficient Reference

How to Use the Simulator

1. Open the Newton's Laws simulator.
2. Select the law to explore: Law 1 (inertia diagram), Law 2 (F=ma calculator), or Law 3 (action-reaction).
3. For Law 2: enter mass, applied force, and friction coefficient. The simulator shows the force diagram and calculates net force and acceleration.
4. For Law 3: enter the action force to see the equal and opposite reaction force displayed on both objects.

The Second Law in Depth

The net force is what matters — not the applied force. Friction always opposes motion:

F_net = F_applied − f = F_applied − μmg

Then: a = F_net / m

Example: A 20 kg box on a wood floor (μ = 0.3) pushed with 100 N:

• Friction force: f = 0.3 × 20 × 9.81 = 58.86 N
• Net force: 100 − 58.86 = 41.14 N
• Acceleration: a = 41.14 / 20 = 2.06 m/s²

Real-World Applications

Car braking (First Law)

Without brakes, a moving car would continue at constant velocity forever (First Law). Brakes apply a friction force that creates a net force opposing motion, decelerating the car. Antilock braking systems (ABS) modulate brake force to maximize friction without locking the wheels.

Rocket propulsion (Third Law)

A rocket expels hot gas backward at high velocity (action). The gas exerts an equal and opposite force on the rocket forward (reaction). There is no need for the gas to push against anything — space is empty. The rocket and the exhaust gases push on each other.

Walking (Third Law)

When you push backward on the ground with your foot (action), the ground pushes you forward (reaction). Without friction between your shoe and the ground, the reaction force would have no horizontal component and you could not move forward — which is why walking on ice is so difficult.

Common Questions

If action equals reaction, why do things move?

Action and reaction forces act on different objects, so they cannot cancel each other. When a horse pulls a cart (action on cart), the cart pulls the horse backward (reaction on horse). The horse moves forward because its feet push on the ground, and the ground's reaction force on the horse exceeds the cart's pull. Net force on the horse = ground reaction − cart tension.

What is static vs kinetic friction?

Static friction acts before an object begins to move and can be up to μ_s × mg. Kinetic (sliding) friction acts once the object is moving and equals μ_k × mg. Static friction is typically higher than kinetic, which is why it takes more force to start sliding a box than to keep it sliding.