What is free fall?
A force is a push or a pull. Many forces act around us: gravity, friction, the push of a spring, the push of air.
A body is in free fall when gravity is the only force acting on it. A stone dropped from a bridge is very close to free fall. Air pushes on it only a tiny bit.
In free fall the body does not move at a steady speed. It speeds up. It speeds up by the same amount every second. Motion like this is called uniformly accelerated motion. (Acceleration means how fast the speed changes.)
The acceleration due to gravity, g
Near the Earth's surface, a falling body gains about 9.8 m/s of speed every second. We write this as g ≈ 9.8 m/s². For easy sums we often use g ≈ 10 m/s².
- After 1 s: speed ≈ 9.8 m/s
- After 2 s: speed ≈ 19.6 m/s
- After 3 s: speed ≈ 29.4 m/s
Heavy and light fall together
Gravity pulls a heavy ball harder. But a heavy ball is also harder to speed up. The two effects cancel exactly. So g is the same for every mass. About 400 years ago Galileo argued this, and today we can see it in a vacuum tube (a tube with the air pumped out).
g is different on other worlds
The Moon pulls more weakly: g ≈ 1.6 m/s². On Mars g ≈ 3.7 m/s², on Jupiter g ≈ 24.8 m/s².
Equations of free fall
For a body dropped from rest (starting speed 0), after time t:
- speed: v = g t
- distance fallen: h = ½ g t²
- speed after falling h: v² = 2 g h
In the 1st, 2nd, 3rd and 4th second the body falls distances in the ratio 1 : 3 : 5 : 7. That is why the photos in the 3D get further apart.
A body thrown up slows down by 9.8 m/s every second, stops for a moment at the top, then falls back. Going up and coming down take the same time (without air).
Air resistance and weight
Air resistance is the push of air against a moving body. It is bigger for wide, light things (a feather, a sheet of paper, a parachute) and grows as the body goes faster. When air resistance becomes equal to gravity, the body stops speeding up. It then falls at a steady terminal speed.
Weight is the force with which gravity pulls a body. W = m × g. Mass (m) is in kilograms; weight (W) is a force, in newtons (N). A 50 kg student weighs 50 × 9.8 = 490 N on Earth but only 50 × 1.6 = 80 N on the Moon. The mass stays 50 kg everywhere.
Try it at home
- Hold a book and a flat sheet of paper at the same height. Drop them. The paper is slower: air holds it back.
- Now put the paper flat on top of the book and drop them together. The book pushes the air away, so the paper falls as fast as the book.
- Crumple the paper into a tight ball and drop it next to the book. They land almost together!
Then open the 3D, choose the Moon, and press Drop. How long does the 20 m fall take now?
Key formulas and definitions
- v = g t (dropped from rest)
- h = ½ g t²
- v² = 2 g h
- W = m × g
- g ≈ 9.8 m/s² on Earth (≈ 10 m/s² for quick sums)
Worked examples
1. A stone is dropped from a bridge. What is its speed after 3 s? (g = 9.8 m/s²)
v = g t = 9.8 × 3 = 29.4 m/s.
2. How far does the stone fall in those 3 s?
h = ½ g t² = ½ × 9.8 × 3² = 4.9 × 9 = 44.1 m.
3. What is the weight of a 60 kg person on Earth (g = 9.8 m/s²)?
W = m g = 60 × 9.8 = 588 N.
4. The same 60 kg person goes to the Moon (g = 1.6 m/s²). Find the mass and the weight.
Mass stays 60 kg. Weight = 60 × 1.6 = 96 N, about one sixth of the Earth weight.
5. A ball is dropped from 20 m. How long does it take to reach the ground? Use g = 10 m/s².
h = ½ g t² → 20 = 5 t² → t² = 4 → t = 2 s.
6. With what speed does that ball hit the ground?
v = g t = 10 × 2 = 20 m/s. Check with v² = 2gh = 2 × 10 × 20 = 400, so v = 20 m/s.
7. A ball is thrown straight up at 15 m/s. How long until it stops at the top? (g = 10 m/s²)
It loses 10 m/s each second, so time = 15 ÷ 10 = 1.5 s.
Common mistakes
- Thinking heavy things fall faster. Without air, all bodies have the same acceleration g.
- Mixing up mass and weight. Mass is in kg and does not change; weight is a force in N and depends on g.
- Saying the speed of a falling body is 9.8 m/s. It is the speed that grows by 9.8 m/s every second.
- Forgetting to square t in h = ½ g t². Doubling the time makes the distance four times bigger.