# Acceleration due to gravity

By A Good Student Abstract The acceleration due to gravity, g, was determined by dropping a metal bearing and measuring the free-fall time with a pendulum of known period. The measured value is 9.706 m/s2 with a standard deviation of 0.0317, which does not fall within the range of known terrestrial values. Centrifugal forces and altitude variations cannot account for the discrepancy. The calculation is very sensitive to the measured drop time, making it the likely source of error. (Short, sweet and to the point. I give the result, method and comment on its agreement or validity.) Theory (First, some background. Be sure to cover any non-numerical aspects of the theory that you wish to address. ) The acceleration due to gravity is the acceleration experienced by an object in free-fall at the surface of the Earth, assuming air friction can be neglected. It has the approximate value of 9.80 m/s2, although it varies with altitude and location. The gravitational acceleration can be obtained from theory by applying Newton’s Law of Universal Gravitation to find the force between the Earth and an object at its surface. Newton’s Law of Universal Gravitation for the force between two bodies is (You may write the equations in by hand.)

where m1 and m2 are the masses of the bodies, r12 is the distance between the centers of mass of the bodies, and G is the Universal Gravitational Constant which has a current accepted value of 6.673 × 10-11 Nm2/kg2. The force between the Earth and a mass, m, would be where ME and RE are the mass and radius of the Earth, respectively. For a particular location, G, ME, and RE are constant and may be grouped under a single constant, g.

For obvious reasons, g is sometimes called the local gravitational constant. It will be numerically equivalent to the acceleration due to gravity on a spherical, non-rotating planet. (If one evaluates the above using