Why do heavy and light objects fall at the same rate?
Gravity pulls harder on a heavier object, but a heavier object also has more mass to get moving, and the two grow in exact proportion. So without air resistance every object near Earth's surface speeds up at the same rate, g ≈ 9.8 m/s², whatever its mass.
More pull, but more mass to move
Two separate facts meet here. The force of gravity on an object, its weight, is W = mg, so doubling the mass doubles the pull. Newton's second law says acceleration is force divided by mass, a = F/m, so doubling the mass also halves how much any given force can speed it up.
Put the two together and the mass cancels: a = mg/m = g. The heavier object gets a bigger push and is exactly that much harder to accelerate. This works because the mass that gravity pulls on and the mass that resists acceleration are the same quantity, a fact experiments have confirmed to very high precision and that Einstein later built general relativity on.
A worked drop
Drop a 1 kg ball and a 10 kg ball from 20 m, ignoring air. The forces on them are 9.8 N and 98 N, but both accelerations are 98/10 = 9.8/1 = 9.8 m/s². The fall time comes from h = ½gt², so t = √(2h/g) = √(40/9.8) ≈ 2.0 s for both, and each hits the ground at v = gt ≈ 19.8 m/s.
On the Moon, where g is about 1.6 m/s², the Apollo 15 astronaut David Scott dropped a hammer and a feather together. With no air to slow the feather, they landed at the same moment.
Where air resistance changes the answer
In air, a falling object also feels drag, D, which depends on its speed, shape and size but not on its mass. The net force is mg − D, so a = g − D/m. For the same drag, a heavier object loses less of its acceleration, which is why a bowling ball beats a beach ball of the same size. Each object speeds up until drag equals its weight and then falls at a steady terminal velocity.
Mistakes that cost points on exams:
- Saying the heavier object falls faster in a vacuum. It does not.
- Mixing up force and acceleration: the heavier object has the bigger force but the same acceleration.
- Setting a = 0 at the top of a throw. The velocity is zero there; the acceleration is still g, downward.
- Forgetting that acceleration is the rate of change of velocity, a derivative.
Watching the forces cancel
In Isotoon you can type a question like "Why does a heavier object not fall faster?" and get a short animated video. A good one would draw both balls with force arrows that grow with mass while their acceleration arrows stay the same length, then add air and show the light ball's drag catching up with its weight. For more of the course, see physics and AP Physics 1.
Questions
- Does a heavier object fall faster in real life?
- Sometimes, because of air. Drag does not depend on mass, so it slows a light object more than a heavy one of the same shape and size. Without air, they fall together.
- Why is g the same for every object if the force of gravity is different?
- Because acceleration is force divided by mass. The force of gravity is mg, so dividing by m leaves g. The larger force on a heavier object is exactly offset by its larger mass.
- Is g exactly 9.8 m/s² everywhere on Earth?
- No. It ranges from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles and drops slightly with altitude. Most courses use 9.8 or 9.81 m/s², and some allow 10 for quick estimates.