# How does air drag affect the motion of dropped objects?

Which weighs more, the bowling ball or soccer ball? You can use your hands to hold first one ball and then the other. You’ll notice that you have to exert a much larger upward force to hold the bowling ball at rest. From Newton’s First Law, if an object is at rest then the net force on it is zero. That is, the downward force of gravity has the same strength as the upward force of your hands. So, you can conclude that the force of gravity, the weight, of the bowling ball is greater than that of the soccer ball.

Galileo was said to have dropped a pressing iron and a wooden ball from the Tower of Pisa and found that they arrived at the bottom at the same time. He also argued that if you tied two wooden balls together, thus doubling the mass, they would obviously fall at the same rate as they would have not tied together.

How can we understand this result? When you drop the ball, the force of gravity is the only force on it, so a = Fgravity/m. An object with a larger force on it will accelerate faster than one with a smaller force, but only as long as the masses are equal. If the forces are equal but the masses different, then the object with greater mass will accelerate more slowly. As described above, because the force of gravity is proportional to the mass, the two effects cancel, and a = g for all masses.

Air drag adds a second force exerted on the object that is in the direction opposite its motion. The net force is the difference between the downward force of gravity and the upward force of air. As was discussed above, the force of the air increases as the speed increases. Therefore, as the object falls and gains speed, the upward force increases. At some time it will equal the downward force and there will be no net force on the object. So, according to Newton’s First Law, the object’s speed will now become constant. This constant velocity is called the terminal velocity.

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