Gravity & Free Fall

Let go of something and it drops — no coincidence, that is gravity: any two masses attract each other. The $F = ma$ from Force & Newton's Laws describes exactly this push and pull, and Earth, enormous and right beneath you, dominates daily life.

How hard does Earth pull?

At the surface, every kilogram of matter is pulled toward the center with about 9.8 newtons. That number is called $g$ :

1 kg → about 9.8 N;
50 kg → about 490 N.

Step on a scale and the reading is precisely this force.

Free fall: faster every second

With no air resistance, a falling object gains about 9.8 m/s of speed every second:

$v = gt$

After 1 second: 9.8 m/s. After 2: 19.6 m/s. After 3: 29.4 m/s. This "same gain every second" motion is uniform acceleration — the acceleration from Speed & Motion is $g$ here. The distance fallen:

$d = \frac{1}{2}gt^2$

How far in two seconds

$d = \frac{1}{2} \times 9.8 \times 2^2 = 19.6$ meters. Not $9.8 \times 4 = 39.2$ — that $\frac{1}{2}$ matters, because the speed starts at zero and builds up.

Mass and weight

Mass is how much matter an object contains (in kg) — it never changes. Weight is the pull a planet exerts on it (in N) — it changes with the planet:

$W = mg$

The Moon's pull is roughly one sixth of Earth's, $g \approx 1.6$ m/s².

Does your weight survive the Moon trip

A 50 kg astronaut: on Earth $W = 50 \times 9.8 = 490$ N; on the Moon $W = 50 \times 1.6 = 80$ N. The weight shrinks dramatically, but the mass is still 50 kg — the person did not get smaller, the Moon just pulls more gently.

With air in the way

On Earth a feather flutters while a stone plummets — air resistance drags on the feather. In 1971 an astronaut on the Moon (which has no air) released a hammer and a feather together, and both hit the ground at the same instant. In a vacuum, everything falls alike. Where air resistance is strong — think a skydiver before the chute opens — drag grows until it balances gravity, and the speed stops increasing. That speed is the terminal velocity, about 200 km/h for a skydiver.

One story, two ledgers

Falling is height being traded for speed: potential energy becomes kinetic energy in the bookkeeping of Work & Energy. Tell the story once with forces, once with energy — the two accounts should balance.

Check yourself

Quick quiz

1. In free fall, how far does an object fall in 2 seconds?
2. What does a 50 kg astronaut weigh on the Moon?
3. In a vacuum the feather and hammer land together because…