# How do these factors affect the free fall of objects?

Take an example of two balls of different masses being dropped from about 250 meters from the ground.

How do the following factors affect free fall:

1. Air resistance.
2. Absence of air resistance.
3. Conduction of experiment on the moon.

For factor 2, I believe that they should fall at an equal rate, one of the reasons being that the force on heavier ball is greater than the second's however it has more inertia balancing it out.

• You have it backwards. And Google "Galileo". – Hot Licks Apr 3 '15 at 12:56
• @HotLicks: Blatantly off-topic, but is your username a parody of the brand "Horlicks"? – Vatsal Manot Apr 3 '15 at 13:01
• @VatsalManot - Nope. – Hot Licks Apr 3 '15 at 13:05

Here is an extremely simple explanation:

1. Force = Mass x Acceleration
2. Force / Mass = Acceleration
3. (Mass x Acceleration due to Gravity) / Mass = Acceleration
4. Acceleration due to Gravity = Acceleration

For further intuition, consider this:

1. The greater the mass, the greater the inertia.
2. The greater the inertia, the greater the difficulty to accelerate the mass.
3. The greater the mass, the greater the weight (i.e. gravitational force acting on the mass).

So, looking at this you can understand that the increased difficulty of acceleration is nullified by the increased gravitational force. They sort of 'cancel' each other out, leaving only acceleration due to gravity behind.

If only the forces of gravity are present, all objects fall at the same rate. This is what one calls equivalence principle. In classical mechanics it shows up in the force law for two particles of gravitating mass $m_G$ and $M_G$, where $M_G$ shall denote the earth's mass. $$m_i \cdot \vec{a} = -G \cdot \frac{m_G \cdot M_G}{|\vec{r} - \vec{r} '|^2 } \cdot \frac{\vec{r} - \vec{r} '}{|\vec{r} - \vec{r} '|}$$ If the inertial mass $m_i$ is equal to the gravitating mass $m_G$ (this is what we observer!), the accelerations is independent of the particle's mass, because they cancel in the equation. Thus, all object fall at the same rate.
Without air resistance all objects are accelerated with gravity $$g = 9.81 \frac{m}{s^2}$$ Only the air causes a "slower" acceleration. This effect depends from the density and shape.