Theory — Newton's Laws and the Net Force
Force and the Free-Body Diagram
A force is a push or a pull, measured in newtons (N). Usually several forces act on an object at once — an applied push, friction, gravity, the support of the ground. A free-body diagram draws each of these as an arrow. The single most important quantity is the net force: the vector sum of all the forces acting on the object.
Forces in the direction of motion are positive; opposing forces are negative.
Newton's First Law — Inertia
An object at rest stays at rest, and an object in motion continues at constant velocity, unless a net force acts on it. So if the net force is zero, the object's velocity does not change — it is either stationary or coasting at constant speed. A moving object slowing down is not "running out of force"; it is being acted on by friction.
Newton's Second Law — F = ma
When the net force is not zero, the object accelerates. The acceleration is proportional to the net force and inversely proportional to the mass. This is the central equation of mechanics.
Units: 1 newton (N) = 1 kg·m/s²
Newton's Third Law — Action–Reaction
For every force there is an equal and opposite reaction force: if you push on a wall with 50 N, the wall pushes back on you with 50 N. The two forces act on different objects, which is why they don't simply cancel.
Friction
Friction is a force that opposes motion (or attempted motion) between surfaces in contact. Kinetic friction — the friction on a sliding object — is proportional to the normal force pressing the surfaces together. On a level surface the normal force equals the weight, mg.
μ = coefficient of friction (no units), g = 9.8 m/s²
Net force zero
Forces are balanced. Acceleration is zero. The object stays at rest or moves at constant velocity (Newton's first law).
Net force non-zero
Forces are unbalanced. The object accelerates in the direction of the net force at a = F_net/m (Newton's second law).
| Change | Effect on acceleration | Reason |
|---|---|---|
| Increase net force (fixed m) | increases proportionally | a = F/m, a ∝ F |
| Increase mass (fixed F) | decreases (a ∝ 1/m) | a = F/m |
| Increase friction | reduces net force → less a | F_net = F_applied − F_friction |
Instructions — Running the Virtual Experiment
The Force Lab tab lets you feel how forces, friction, and mass combine; the Measurements tab provides the quantitative test of F = ma. Record every reading in your lab notebook.
Simulation — Net Force, Friction & Acceleration
Controls
Frictionless · m = 2 kg
Set applied force
| Applied force (N) | Acceleration (m/s²) | a / F (kg⁻¹) |
|---|---|---|
| No readings yet — pick a force and click "Record reading". | ||
Team Questions
Example Lab Report
Sample report demonstrating the expected format and level of detail. Use as a guide for your own submission.
Forces and Motion: Verifying Newton's Second Law
Physics | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Purpose
To investigate the relationship between net force, mass, and acceleration, and to verify Newton's second law (F = ma) by measuring the acceleration produced by a range of net forces on a fixed mass. The lab also examines how friction reduces the net force and how mass affects acceleration.
Theory
The net force on an object is the vector sum of all forces acting on it. By Newton's second law, this net force produces an acceleration proportional to the force and inversely proportional to the mass. On a level surface, kinetic friction opposes motion with a force μmg.
F_net = m·a → a = F_net / m
a ∝ F (fixed m) · a ∝ 1/m (fixed F)
A graph of acceleration versus net force (at fixed mass) is a straight line through the origin whose slope equals 1/m, so multiplying the slope by the mass should give 1.
Calculations — Sample: net force 8 N on a 2 kg mass (frictionless)
Acceleration: a = F_net/m = 8/2 = 4.0 m/s²
Slope of a-vs-F: from (2 N, 1 m/s²) and (10 N, 5 m/s²): slope = (5 − 1)/(10 − 2) = 4/8 = 0.50 kg⁻¹
Check: slope × mass = 0.50 × 2 = 1.00 ✓ (confirms F = ma)
With friction (μ = 0.20, m = 4 kg, F_applied = 20 N): F_friction = μmg = 0.20 × 4 × 9.8 = 7.84 N; F_net = 20 − 7.84 = 12.16 N; a = 12.16/4 = 3.04 m/s²
Results Table — Acceleration vs Applied Force (frictionless, m = 2 kg)
| Applied force (N) | Acceleration (m/s²) | a / F (kg⁻¹) |
|---|---|---|
| 2 | 1.0 | 0.50 |
| 4 | 2.0 | 0.50 |
| 6 | 3.0 | 0.50 |
| 8 | 4.0 | 0.50 |
| 10 | 5.0 | 0.50 |
Mass trial (F = 20 N, frictionless): doubling the mass from 2 kg to 4 kg halved the acceleration from 10 m/s² to 5 m/s², confirming a ∝ 1/m.
Discussion
The acceleration was directly proportional to the net force: each reading of a/F gave the same value, 0.50 kg⁻¹, and the a-versus-F graph was a straight line through the origin. Its slope (0.50 kg⁻¹) multiplied by the mass (2 kg) gave 1.00, confirming F = ma. When the mass was doubled at fixed force, the acceleration was halved, verifying the inverse relationship a ∝ 1/m.
Adding friction reduced the net force and therefore the acceleration. Below the point where the applied force exceeded the friction force, the net force was zero and the object did not move, illustrating Newton's first law. A crate moving at constant velocity likewise has zero net force, meaning the applied push exactly balances friction.
Conclusion
The experiment verified Newton's second law. Acceleration was proportional to net force (slope × mass = 1) and inversely proportional to mass, and friction was shown to subtract from the applied force to set the net force. Zero net force produced zero acceleration, consistent with Newton's first law.
Practice Questions
Show all work and include units in your answers.