## MEASURING THE ACCELERATION DUE TO GRAVITY

The acceleration due to gravity, usually labelled g, is a constant, with a value at sea level of about

980.62 cm/s2 . By measuring the change in the period of a simple pendulum as a function of

its length, you can calculate the value of g using quadratic regression.

### THEORY

The period, T, of a pendulum is the time it takes for one complete swing

(from point A in the diagram back to point A)

A

The period of a pendulum depends on its length, l, according to

If  both sides are squared, we get    .

Now multiply both sides by g and flip the two sides of the equation, getting  .

Finally, divide both sides by , getting the quadratic function    .

This is a quadratic function  with  .

Now if we collect data for the periods of pendulums of different lengths, we can fit the data to

a quadratic function, find a value for the constant a and then use the value of a to calculate g.

### PROCEDURE

1. For a pendulum of length 70 cm, measure the time it takes for 20 complete swings.

2. Calculate the period. Repeat two more times. Calculate the average period (one decimal).

3. Repeat steps 1 and 2 for pendulums of length 60 cm, 50 cm, 40 cm ,30 cm and 20 cm.

4. Draw a graph of l versus T. Put T along the horizontal. Remember all the labels, Put on a title.

5. On the TI-83+, enter the values for T in L1 and l in L2 .

6. Press the STAT key, then move over to the CALC menu and select #5, QuadReg.

7. Use the value of a given by the regression to calculate g correct to the nearest cm/s2.