A P H Y S I C S L E S S O N
Forces, Motion
& Gravity
Understanding $F = ma$ — the formula that explains how everything moves
$F = m\,a$
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CHAPTER 1   FOUNDATIONS
What is a Force?
A force is simply a push or a pull on something.
→

P U S H

Shoving a shopping cart down the aisle

←

P U L L

Tugging a wagon behind you

↓

G R A V I T Y

Earth pulls an apple down to the ground

Forces can speed things up, slow them down, or change their direction.
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CHAPTER 2   THE BIG IDEA
Newton's Second Law
$F$ $=$ $m$ $\cdot$ $a$
Force = Mass × Acceleration
If you know two of them, you can find the third.
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CHAPTER 2   THE BIG IDEA
Breaking It Down
$F$

Force

Newtons (N)

How hard you push or pull. One Newton is about the weight of a small apple.

$m$

Mass

Kilograms (kg)

How much stuff is in an object. A bowling ball has more mass than a beach toy.

$a$

Acceleration

m/s²

How quickly speed is changing. Flooring the gas in a car is high acceleration.

Bigger force → bigger acceleration.   Heavier object → needs more force to move the same way.
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CHAPTER 2   THE BIG IDEA
$F = m \cdot a$ in Real Life
Same formula, three familiar situations.
Pushing a shopping cart
A gentle push gives small acceleration. Push harder, and the cart speeds up faster.
bigger F → bigger a
Bike vs. truck
Push a bike and a truck with the same force. The bike zooms; the truck barely moves.
bigger m → smaller a
Kicking a ball
A soft tap barely moves the ball. A strong kick sends it flying.
bigger F → bigger a
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CHAPTER 3   GRAVITY
Gravity: A Force That Pulls

Every object with mass pulls on every other object.

The Sun pulls the Earth.
The Earth pulls the Moon.
The Earth pulls you — and you pull the Earth back (just very, very gently).

Two rules of gravity
1. More mass → stronger pull
2. Farther away → weaker pull
Sun
← gravity pulls —
Earth
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CHAPTER 3   GRAVITY
Gravity on Earth
When you drop something, Earth's gravity makes it fall faster and faster.
On Earth, $a = 9.80665$ m/s²
$F$ $=$ $m$ $\cdot$ $9.80665$
This force is what we call weight.
Every second something falls, it gets 9.81 m/s faster.
Try it: a 2 kg ball
Force of gravity on it?
$F$ $=$ $2$ $\cdot$ $9.80665$ $=$ $19.61\;\text{N}$
After 1 second of falling?
$v$ $=$ $9.81\;\text{m/s}$ ($\approx 35\;\text{km/h}$)
After 2 seconds?
$v$ $=$ $19.61\;\text{m/s}$ ($\approx 71\;\text{km/h}$)
It keeps getting faster every second.
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CHAPTER 3   GRAVITY
Newton's Law of Universal Gravitation
$F$ $=$ $G$ $\displaystyle\frac{\textcolor{teal}{m_1\,m_2}}{\textcolor{gold}{r^{2}}}$
$G$

A tiny number (the gravity constant)

$m_1 \cdot m_2$

The two masses multiplied together

$r$

The distance between them

Double the distance → gravity becomes 4× weaker (because $r$ is squared).
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CHAPTER 3   GRAVITY
A Surprising Discovery
“Heavy and light things fall at the same speed.”
A bowling ball and a feather, dropped in a vacuum, land at the exact same time.
Why? The math shows us:
$F = m\,a$
Newton's 2nd Law
→
$F = m\,g$
Gravity's pull
→
$m\,a = m\,g$
Both equal F
→
$a = g$
Mass cancels out!
No matter the mass, everything on Earth accelerates at the same $9.80665$ m/s².
Galileo tested this by dropping balls from the Leaning Tower of Pisa about 400 years ago.
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CHAPTER 4   CODE IT
Code Example 1: A Falling Ball
Using $F = m \cdot a$ to simulate gravity pulling a ball toward the ground.
gravity.js 
let y = 0;          // position (how high up)
let v = 0;          // velocity (speed + direction)
const m = 1;        // mass in kg
const g = 9.80665;  // Earth's gravity

function fall(dt) {
  const F = m * g;  // F = m · a
  const a = F / m;  // a = F ÷ m
  v += a * dt;      // speed up each tick
  y += v * dt;      // move by current speed
}

What happens

Tick 0 → v = 0
(ball stationary)
Tick 1 → v = 9.81
(1 sec later)
Tick 2 → v = 19.61
(2 sec later)
Speed keeps growing!
Notice: mass cancels out — $a = g$. Any ball falls the same way.
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CHAPTER 4   CODE IT
Code Example 2: Two Planets Pulling
Using Newton's law of gravitation: $F = G \cdot m_1 \cdot m_2 / r^2$
planets.js 
const G = 1;  // gravity strength

function pull(a, b) {
  const dx = b.x - a.x;
  const dy = b.y - a.y;
  const r = Math.sqrt(dx*dx + dy*dy);
  // F = G · m1 · m2 / r^2
  const F = G * a.m * b.m / (r * r);
  // a = F / m  (from F = ma)
  a.ax += F * dx / r / a.m;
  a.ay += F * dy / r / a.m;
}
A
→ ←
B
They pull each other with equal and opposite force.
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T H R E E   B I G   I D E A S
What You've Learned
1
$F = m \cdot a$

Push harder, it speeds up faster. Heavier things need more force.

2
Gravity is just a force

Everything with mass pulls. More mass, stronger pull.

3
Math becomes code

JavaScript can simulate planets and falling balls.

Now go experiment in the gravity simulator!
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