3.2 Forces & Newton's Laws

Newton's Laws of Motion explain why objects move the way kinematics describes — they connect force, mass, and acceleration into one predictable relationship. Nearly every NAPT question about a net force, a force needed to accelerate an object, or friction acting on a moving object comes down to the same core equation: F = ma. This section covers Newton's three laws with real-world examples, how to read a free-body diagram, how to calculate net force, and the basics of friction — the resistive force that shows up in almost every real mechanics problem.

Newton's First Law: Inertia

Newton's First Law of Motion (the law of inertia) states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity in a straight line, unless acted on by a net external force. Inertia is the tendency of an object to resist a change in its motion, and mass is the measure of inertia — the more mass an object has, the more force is needed to change its velocity.

Real example: A loose tool sitting on a workbench stays put until something pushes it. But if the deck beneath it suddenly turns or lurches, the tool — following its own inertia — tends to keep moving in a straight line relative to the room, appearing to slide toward whichever side the deck turned away from. Nothing mysterious pushed it; its own inertia simply resisted the change in direction that the deck underwent.

Newton's Second Law: F = ma

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:

F_net = m × a

Where F_net is the net force in newtons (N), m is mass in kilograms (kg), and a is acceleration in meters per second squared (m/s²). One newton is the force needed to accelerate a 1 kg mass at 1 m/s². Rearranged, the same equation solves for mass (m = F/a) or acceleration (a = F/m) whenever the other two variables are known.

Worked Example 1: Force Needed to Accelerate

A tow line must accelerate a 500 kg boat at 0.8 m/s² across calm water (ignoring drag for this problem). Find the force the tow line must apply.

F = ma = (500 kg)(0.8 m/s²) = 400 N

Worked Example 2: Finding Acceleration From Force

A 1,200 kg small craft's engine produces 3,600 N of net forward thrust. Find its acceleration.

a = F / m = 3,600 N / 1,200 kg = 3 m/s²

Newton's Third Law: Action and Reaction

Newton's Third Law states that for every action force, there is an equal and opposite reaction force, and the two forces act on two different objects.

Real example: A sailor pushing off a pier to board a small boat pushes backward on the pier (the action force); the pier pushes forward on the sailor with equal force (the reaction force), propelling the sailor toward the boat. A ship's propeller works the same way — it pushes water backward (action), and the water pushes the ship forward (reaction). That reaction force is literally what moves the ship.

Exam trap to avoid: action-reaction pairs act on different objects, so they never cancel out for a single object's own motion. The forces that determine whether one object accelerates are only the forces acting on that object.

Free-Body Diagrams in Table Form

A free-body diagram isolates a single object and lists every force acting on it — direction and, where known, magnitude — without drawing the rest of the surrounding scene. You do not need to sketch arrows to use this idea on the exam; a simple table captures the same information.

Example 1 — A toolbox at rest on the flight deck (20 kg):

Because the box has zero vertical acceleration, the net vertical force is zero, so the normal force exactly balances weight. Any time an object rests on a flat, unaccelerated surface with no other vertical forces acting on it, N = mg.

Example 2 — A crate being pulled across the deck against friction:

Net Force: Combining Multiple Forces

When more than one force acts on an object, the net force is the vector sum of all of them: forces pointing the same way add together, and forces pointing opposite ways subtract.

Worked Example 3: Net Force With Friction

A 50 kg crate is pulled across a steel deck by a rope with 300 N of tension. Friction opposes the motion with a force of 120 N. Find the crate's acceleration.

F_net = 300 N − 120 N = 180 N

a = F_net / m = 180 N / 50 kg = 3.6 m/s²

Friction Basics

Friction is the force that resists relative motion (or attempted motion) between two surfaces in contact. Two kinds matter at this level:

• Static friction resists the start of motion between two surfaces that are not yet sliding; it adjusts up to a maximum value right before the object breaks loose and starts to slide.
• Kinetic friction acts once the surfaces are already sliding, and is usually smaller than the maximum static friction — it is harder to start something sliding than it is to keep it sliding.

The friction force formula:

f = μN

Where f is the friction force, μ (the Greek letter mu) is the coefficient of friction — a unitless number that depends on the two specific surfaces in contact — and N is the normal force pressing the surfaces together.

Worked Example 4: Friction From a Coefficient

A 50 kg crate rests on a steel deck with a kinetic coefficient of friction μk = 0.3. Find the friction force resisting its sliding.

N = mg = (50)(9.8) = 490 N

f = μN = (0.3)(490) = 147 N

Section Takeaways

• Newton's First Law (inertia): an object's motion does not change unless a net external force acts on it; more mass means more resistance to that change.
• Newton's Second Law: F_net = ma — net force equals mass times acceleration; rearrange to solve for force, mass, or acceleration.
• Newton's Third Law: every action force has an equal, opposite reaction force acting on a different object, so action-reaction pairs never cancel for a single object.
• A free-body diagram — even one described as a table — isolates one object's forces: weight down, normal force up, plus any applied force and friction.
• Friction force equals the coefficient of friction times the normal force (f = μN); static friction is generally larger than kinetic friction.