A value for g

This is a Practical

I'm just going to copy everything from a book, okay?

Aim
To determine the rate of acceleration due to gravity using the motion of a pendulum.

Equipment

  • Retort Stand
  • Bosshead and Clamp
  • Some length of string (1~1.5m)
  • Pendulum Bob (Some sort of attachable mass is fine.)
  • Stopwatch
  • Metre ruler
  • 2 $\frac{1}{2}$Rubber Stoppers

Theory
When a simple pendulum swings with a small angle (less than 10゜to the vertical), the mass on the end performs a good approximation of the back and forth motion called simple harmonic motion. The period of the pendulum, that is, the time taken to complete a single fulll back and forth swing depends upon just two variables:

  • The length of the string
  • The rate of acceleration due to gravity.

The formula for the period is as shown:

(1)
\begin{align} T = 2\pi\sqrt{\frac{l}{g}} \end{align}

where:

  • T = period of the pendulum (s)
  • l = length of the string (m)
  • g = rate of acceleration due to gravity ($ms^{-2}$)

Method

  1. Set up the retort stand and clamp on the edge of a desk shown below.
  2. Tie one end of the string to the pendulum bob.
  3. Clamp the string between the stoppers and adjust the length (Bottom of stopper to middle of bob) to a desirable amount (0.9~1.5 cm is suggested.)
  4. Record this length in the results table.
  5. Set the pendulum to swing gently (Less than 10゜from vertical is desirable, 30゜is maximum) and use the stopwatch to time 10 complete back and forth swings. Be sure to start and stop the stopwatch at the furthest point or the closest point and not the middle.
  6. Enter the time for 10 swings into the results table.
  7. Repeat steps 3 to 6, shortening the string by 5~10cm until enough results is obtained.

Sample Results

Length of pendulum (m) Time for 10 Oscillations (s) Period (s) Period squared ($s^2$)
1.00 21.03 2.103 4.423
0.80 18.01 1.801 3.244
0.60 15.77 1.577 2.487
0.40 12.92 1.292 1.669

You should draw up a graph. Plot $T^2$ on the y axis and the length of the string on the x axis.