Freely Falling Bodies
Simple Explanation
A body falls freely when gravity is the only force acting on it — no air resistance, no support. Because Newton's second law (F = ma) and weight (W = mg) both apply, EVERY freely falling object accelerates at exactly g, regardless of its mass — a heavier object has more weight pulling it down, but also more inertia resisting that pull, and the two effects exactly cancel.
Why Do We Need It?
This connects three ideas from this chapter — Newton's second law, weight, and Newton's laws of motion — into a single, surprising result: in the absence of air resistance, a feather and a hammer fall at exactly the same rate.
Worked Example
Show that mass cancels out for a freely falling body
Show, using F = ma and W = mg, that the acceleration of any freely falling object is g, independent of its mass.
Why Does This Work?
The mass cancels precisely because BOTH the force causing the fall (weight, mg) and the object's resistance to accelerating (inertia, m in F = ma) scale with the same mass — so a more massive object is pulled down harder, but resists that pull just as much more, leaving the acceleration unchanged.
Real-Life Example
Apollo 15's hammer-and-feather demonstration
On the airless Moon, astronaut David Scott dropped a hammer and a feather at the same time, live on camera.
With no air resistance to slow the much lighter feather, both objects hit the lunar surface at exactly the same moment — a direct demonstration that freely falling acceleration does not depend on mass.
Practice
A 2 kg ball and a 10 kg ball are dropped from the same height in a vacuum (no air resistance). Which hits the ground first?
MediumCommon mistake
Assuming heavier objects always fall faster — this is only true in the presence of air resistance, which affects light, large-surface-area objects (like feathers) far more than dense, compact ones; true free fall (no air) is mass-independent.
Quick Review
- A freely falling body has only gravity (weight) acting on it — no air resistance, no support.
- F = ma and W = mg together show that a = g, independent of mass.
- This is why a hammer and a feather fall together on the Moon (no air).