Newton's Laws in Practice

A guided lesson applying Newton's three laws of motion to real-world problems, with free body diagrams and worked examples.

Why Newton's Laws?

Newton's laws are the foundation of mechanics. They explain everything from a ball rolling on the floor to satellites orbiting Earth.

First Law: Inertia in Action

An object at rest stays at rest. A moving object keeps moving unless a net force acts on it.

Note

A passenger lurches forward when a car brakes — that's inertia. The car slows, but the passenger's body wants to keep moving.

Second Law: F = ma

Net Force

\sum F = ma

Sum of all forces = mass × acceleration

1
Draw a free body diagram
Show all forces on the object: weight, normal, friction, applied.
2
Choose a coordinate system
Positive x = direction of motion, positive y = upward.
3
Write Newton's second law for each axis
$\sum F_x = ma_x$ and $\sum F_y = ma_y$
4
Solve for the unknown
Substitute known values and solve.

Block on flat surface: applied force 30 N, mass 6 kg, friction 6 N. Find acceleration.

$\sum F = 30 - 6 = 24 \text{ N}$

$a = F/m = 24/6 = 4 \text{ m/s}^2$

Free body diagram showing all forces on the block

Third Law: Action-Reaction

Every force has an equal and opposite reaction force.

Warning

Action-reaction pairs act on different objects. They never cancel each other within the same system.

Real world: car seatbelts (First Law)

In a car crash, the vehicle stops suddenly but passengers continue moving forward at the original speed — Newton's First Law (inertia). A seatbelt applies a backward force to stop the passenger, protecting them from hitting the windscreen. Airbags work on the same principle, extending the stopping time and reducing the average force.

Real world: rocket launch (Second and Third Laws)

A 500 000 kg rocket applies 7 000 000 N of thrust. Net force (subtracting weight) determines acceleration via $a = F/m$ . At launch, the rocket expels exhaust gases downward; by the Third Law, the gases push the rocket upward with equal force. Every rocket launch is a direct demonstration of $F = ma$ and action-reaction pairs.

Real world: sports biomechanics — sprinting

A sprinter's shoe pushes backward on the track with force $F$ ; the track pushes the sprinter forward with the same force (Third Law). A 70 kg sprinter accelerating at $2\text{ m/s}^2$ requires a net force of $F = 70 \times 2 = 140\text{ N}$ . Coaches use Newton's Second Law to set training targets for stride power.

Tip Always draw a free body diagram before applying Newton's Second Law. Label every force with its magnitude, direction, and the object it acts on. Net force =

\sum F

, not just the largest force.

Practice Problems

A 4 kg box is pulled with 20 N on a frictionless surface. Find acceleration.

Show answer

a = F/m = 20/4 = 5 m/s²

Two forces act on a 5 kg object: 15 N right and 5 N left. Find acceleration.

Show answer

Net F = 10 N right. a = 10/5 = 2 m/s² right

What is the weight of a 70 kg person on Earth (g = 9.8 m/s²)?

Show answer

W = mg = 70 × 9.8 = 686 N