Force & Newton's Laws

An apple falls, a car brakes, a rocket lifts off — underneath each is the same thing: force. Three hundred years ago Newton wrote down three laws that explain exactly why things move the way they do, and they still open every physics book today.

Force: a push or a pull

A force is one object pushing or pulling another, measured in newtons (N) — holding up an apple takes about 1 N. Forces have direction, and all the forces on one object combine into a single net force:

Net force 0 (balanced forces): the object stays still or keeps moving in a straight line at constant speed — like a tug-of-war deadlock or a car cruising steadily;
Net force not 0: the motion changes — speeding up, slowing down or turning.

The most familiar forces are gravity (Earth pulling down) and friction (opposing sliding between surfaces). Speed & Motion described how fast; here we explain why fast changes.

The first law: inertia

Newton's first law: with no force or zero net force, an object stays at rest or keeps moving in a straight line at constant speed. This reluctance to change motion is called inertia.

When a car brakes hard, the car stops but your body tries to keep going at the old speed — the seatbelt takes on that inertia and pulls you back into your seat. Wearing a seatbelt is not a formality; it is the first law protecting you.

The second law: F = ma

$F = ma$

The bigger the net force, the fiercer the acceleration; the bigger the mass, the harder it is to get moving. An empty shopping cart moves at a light touch — a loaded one needs real effort. Same force, more mass, less acceleration.

Worked example: accelerating a car

A car of mass $m = 1000$ kg needs to accelerate at $a = 2\ \mathrm{m/s^2}$ . What net force is required?

$F = ma = 1000 \times 2 = 2000\ \mathrm{N}$

Load it up to 2000 kg and the same 2000 N buys only $a = F \div m = 1\ \mathrm{m/s^2}$ — the heavier the car, the lazier it feels.

The third law: action and reaction

Forces never come alone: when A pushes B, B pushes back on A just as hard in the opposite direction. Swimming, your hands push water backward and the water pushes you forward; a rocket blasts gas downward and the gas shoves the rocket upward. The pair acts on two different objects, which is why they never cancel out.

Weight and mass

Mass (in kg) is how much stuff an object contains; weight is the pull of gravity on it (in N):

$W = mg$

with $g \approx 9.8$ N/kg. Mass stays the same everywhere; weight follows gravity — on the Moon your mass is unchanged but your weight drops to about a sixth.

Worked example: how heavy are you?

A 30 kg student feels a gravitational pull of $W = 30 \times 9.8 = 294$ N on Earth. On the Moon ( $g \approx 1.6$ N/kg) it is only $30 \times 1.6 = 48$ N — yet the mass is still 30 kg. Mass is measured in kg, weight in N; keep them apart. Unit conversion helps here too.

Analyzing forces in three steps

First ask what is pushing or pulling this object, and draw each force (gravity and friction are almost always present); then assign signs by direction; finally add them up. Motion obeys the net force — not any single force.

Check yourself

Quick quiz

1. Braking hard, you lurch forward and the seatbelt holds you. Which law is at work?
2. What net force gives a 1000 kg car an acceleration of 2 m/s²?
3. Roughly what gravitational force acts on a 60 kg person?