Calculating a value for g by a free fall method.

Objective

To measure the acceleration due to gravity by a free fall method.

Theory

An object falling freely under gravity, assuming that air resistance effects can be neglected, obeys the following equation:

s = ut + ½at²(1)

Apparatus

A ball bearing is held vertically above a mechanical plate by means of a small electromagnet. When the current through the magnet is switched off, the ball bearing falls from rest until it hits the plate. An electric stop-clock records the time of fall, since the start signal to the clock is synchronised with the release of the ball-bearing and the stop signal with the closing of a switch actuated by the plate.

Experimental Procedure

1. For a particular value of s, record the fall time t. Take several readings of t for each value of s in order to estimate the error in measuring t.
2. Measure the fall times for 8 values of s. Try to cover as large a range of distances as possible. Consider carefully the value of s (Is there a systematic error possible here?)

Method of Analysis

1. Present your results graphically by plotting t² against s. From the error D[delta]t on t, evaluate the error 2t[delta]t on t² and draw this on each plotted point.
2. Since the ball bearing falls from rest, u = 0. Hence s=½at² or t²=(2/a)s. The gradient of the graph (with s being plotted along the horizontal axis) is therefore 2/a.
3. Find the gradient and the error in the gradient from your graph.
4. Calculate g and the error in g.

Thanks, that was really useful , one small question though, how do you calculate g at the end?