Forces and Motion: Basics

TRY THIS FIRST

Do heavy and light boxes accelerate differently under the same push?

Only the ratio F/m sets the acceleration. Double the force AND the mass together and the box speeds up exactly the same — that's Newton's second law in one line.

→ Test it: try the "Heavy vs Light" preset, then halve both mass and force.

CORE FORMULAS

Newton's Second Law — net force equals mass times acceleration

Kinetic friction force — opposes sliding motion

Net force — applied force minus friction

INCLINE & ATWOOD (STANDARD RESULTS)

Acceleration down a slope with friction

Normal force on an incline of angle θ

Atwood machine acceleration (two hanging masses)

THEORY

Newton's Second Law states that the net force on an object equals its mass times acceleration. Friction opposes motion and depends on the normal force and friction coefficient. Static friction prevents motion up to a maximum threshold; kinetic friction acts during sliding. The force diagram (free body diagram) shows all forces acting on the object, and their vector sum gives the net force.

HOW TO USE

Push the object with the Applied Force slider and watch the free body diagram update in real time. The force chart shows applied force, friction force, and net force side by side. Change the friction coefficient to see different surfaces in action, and tilt the incline to trade kinetic and potential energy back and forth.

LEARNING CARDS

Always Draw the Free Body Diagram

List every force: weight mg↓, normal N⊥surface, friction f‖surface (opposing motion), and the applied push F. Their vector sum is the net force that drives the acceleration.

Static vs Kinetic Friction

Static friction adjusts to prevent motion up to f_s ≤ μ_s N. Once sliding, kinetic friction is constant at f_k = μ_k N and always opposes velocity. Because μ_s > μ_k, it is harder to start a box moving than to keep it moving.

Acceleration Is F/m

A heavier box needs a bigger force to reach the same acceleration, but if you scale force and mass by the same factor the ratio F/m — and therefore the acceleration — is unchanged. Mass measures inertia, the resistance to changing motion.

Energy on a Frictionless Slope

With no friction, mechanical energy is conserved: as the box slides down, gravitational potential energy converts entirely into kinetic energy, then back again. Add friction and that mechanical energy leaks away as heat — watch the Heat bar climb.

WHY IT MATTERS

Vehicle braking distances depend directly on the friction coefficient between tire and road
Ramps and pulleys (Atwood machines) trade force for distance in elevators and cranes
Every structural and mechanical design begins with a free body diagram

🔗 AP Physics 1 alignment: 3.A.1, 3.B.1, 3.B.2 (forces & Newton's laws). NGSS: HS-PS2-1, MS-PS2-1. GCSE: AQA P5.2, P5.3.

ENERGY

KE0.0 J

PE (gravity)0.0 J

Mechanical (KE+PE)0.0 J

Heat (friction)0.0 J

LIVE DATA

a	—	m/s²
v	—	m/s
N	—	N
f	—	N
F_net	—	N
T	—	N
x	—	m

QUIZ

Speed:

Preset:

Applied Force F: 15 N

Object Mass m: 2.0 kg

Friction µ: 0.20

Incline θ: 0°

2nd Mass m₂: 2.0 kg