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?

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/s^{2}) then they will have equal
velocities as they fall, and they will both hit the ground at the
same time.

Suppose object B has a mass of 1 kilogram. The weight of B = (B 's
mass)(g) = 1 kg)(10 m/s^{2}) = 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/s^{2} =
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/s^{2}) = 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/s^{2} = g.

Both A and B have the same acceleration (g = 10
m/s^{2}).

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:

last update November 10, 2007 by JL Stanbrough