Free Fall Explained

The Puzzle

If air resistance is not a factor, we know that 2 objects of different weights fall at the same rate. On the moon, where there is essentially no atmosphere, astronauts once demonstrated that a feather and a hammer fall at the same rate. Here on earth, a book and a paper wad hit the floor at the same time when dropped together. Why?

An Explanation

Newton's Second Law provides the explanation. The acceleration of an object depends on 2 factors:

• the net force on the object.
• the objects mass.

Newton's Second Law says that the acceleration of an object is directly proportional to the net force on it (force doubles - acceleration double) and inversely proportional to its mass (mass doubles - acceleration halves).

For an object in free fall, the net force on it equals its weight (the pull of gravity - the force exerted on it by the Earth) and its weight is proportional to its mass. In other words, if object A has twice the mass of object B, then A also weighs twice as much as B. If A weighs twice as much as B, then the Earth pulls on A twice as hard as it pulls on B, and the net force on A during free fall is twice as much as the net force on B.

However, since A has twice the mass of B, it resists accelerating twice as much as B. These two effects - A has twice the force, but it resists twice as much - cancel each other out, and A has the same acceleration as B in free fall!

If A and B both start falling from rest, and they both have the same acceleration (g = 9.8 m/s²) then they will have equal velocities as they fall, and they will both hit the ground at the same time.

A Simple Numerical Example

Suppose object B has a mass of 1 kilogram. The weight of B = (B 's mass)(g) = 1 kg)(10 m/s²) = 10 Newtons. Since we are not considering air resistance, this is the only force acting on B, so the net force on B is 10 Newtons downward.

Newton's Second Law says that the acceleration of B = (net force on B)/(mass of B) = (10 Newtons)/(1 kilogram) = 10 m/s² = g.

Suppose that object A has a mass of 2 kilograms (twice the mass of B). A's weight = (A's mass)(g) = (2 kg)(10 m/s²) = 20 Newtons. Since this is the only force acting on A as it falls, the net force on A is 20 Newtons.

The acceleration of A = (net force on A)/(mass of A) = (20 Newtons)/(2 kg) = 10 m/s² = g.

Both A and B have the same acceleration (g = 10 m/s²).

An Abstract Explanation

An object of mass m in free fall feels a net force equal to its weight w, where w = mg. By Newton's Second Law, the object's acceleration is: