Uniformly Accelerated Motion Lab

The Goal: To find what the acceleration of gravity on Earth is.

The Method: Dropping tennis balls while timing their fall.

The Theory: The Earth, the Moon, the Sun, you and your brothers and sisters, your cat and/or dog--everything attracts everything else with a force we call gravity. This force is never a repulsion; that is, it never pushes away. It always pulls objects together with a force that depends on the product of their masses and the inverse of the square of the distance between the objects. (Believe me, this will be a mantra by the end of the semester!). The mass condition means that two heavy masses attract each other more than two light masses. It is an important factor, but more important is the distance condition. Inverse square means this: if you double the distance between the two masses, the force of attraction goes down by a factor of four. If you triple the distance, the force goes down by a factor of nine. And if you quadruple the distance, the force diminishes by a factor of sixteen! Clearly this is the more important factor.

However, if we drop objects off a building, the distance from the top of the building to the center of the Earth's mass is about the same as the distance from the bottom of the building to the Earth's center. Therefore, the force of gravity between the Earth and, say, a tennis ball is constant over the fall. According to Newton, the quotient of force and mass is acceleration. More mass means more force, but the ratio of force to mass stays constant, yielding a value we call 'g', the acceleration of gravity. Everything has a 'g', but the force between you and a friend is so small that its 'g' cannot be measured. On the other hand, 'g' on a large planet like Jupiter is two-and-a-half times that on the Earth.

So what is important about g? It determines your weight. Your mass is the same everywhere, but the force of gravitational attraction creates your weight. On the Moon there is as much of you as there is on Earth, but you would weigh one-sixth as much. Therefore, measuring g is an important building block of science.

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