Acceleration of Gravity

If Galileo was correct and all objects accelerate towards the earth at the same rate, then the value of that acceleration will be an important number to measure.

There are a number of ways to determine the acceleration due to gravity:

I. The most direct method would be to drop an object and to record its motion for later measurement:- Choose an object which has considerable density (more precisely, considerable mass and relatively small surface area) so that the wind resistance during its fall will be insignificant.
- Arrange a camera to record a video sequence the fall (including its initial motion) over a known distance.
- Analyze the recorded motion counting the number of captured images in the motion sequence to determine the elapsed time of fall. (Standard video records 30 frames/second but your camera may record images at another rate. Varify your method of measuring time against a known time interval.)
- According to Galileo, the distance fallen from rest, d = 1/2 at
^{2}. Solving for

we get**a****a = 2d / t**. Substitute the distance fallen from rest and elapsed time to determine the acceleration due to gravity.^{2} - But there is an inherent flaw in capturing images separated at finite time intervals. The fall may have started at a time between images, allowing the elapsed time to be long by up to the time between images. It might be more accurate to calculate a speed near the start of the fall but after the first falling interval, v
_{i}, and a later speed near the end of the sequence, v_{f}, and use Galileo's definition of acceleration,**a ≡ v**._{f}- v_{i}/ t

- Using a long, thin string, hang a large mass from a very stationary support.
- Usings swings of small angles, time a large number (~100) round trip swings to determine the average period of the pendulum, T.
- Measure the length of the pendulum from the center of the mass to the stationary support. You may use any convenient unit of length, but using standard units will result in more useful values. (The
**meter**is the universally accepted unit of length.) - Substitute the pendulum's length,
*l*, and its period, T, into the equation and solve to find

.**a**

Finally, record your procedures, measurements, and findings in your journal. **If you need course credit, use your observations recorded in your journal to construct a** formal report

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latest revision 13 February 2010 by D Trapp