# APPEAL 2013

Measuring the local acceleration due to gravity (g) using a simple pendulum

Background

As objects fall towards the Earth, they speed up. Galileo’s surprising discovery was that the mass of an object doesn’t affect how much it speeds up (accelerates) as it falls. Rather, the acceleration depends only on the force that’s making the object fall, i.e. on gravity. But the Earth’s gravity is not the same everywhere; its strength changes depending on how far you are from the centre of the Earth (i.e. your altitude), your distance from the equator, the composition of the ground beneath you and many other things. We will be charting the strength of gravity all over the over the UK (the original idea comes from Australia; see www.aip.org.au/littleg for more information) by looking at an object that falls over and over again: a pendulum. The motion of a pendulum is incredibly stable, and by simply measuring its length and the time it takes to complete one swing (the period), we can work out the strength of the Earth’s gravity at that exact spot.

Equipment you can use at home

Length of fishing wire (or something similar) Washers Bulldog clip Blu-tack Stopwatch Tape measure

Method

1) With a friend or relative, find a doorway, a high chair, bar or tree branch that is as high as you can safely reach and has plenty of space underneath so that your pendulum can swing easily and you can measure its period easily.

2) Cut a length of the fishing wire that will give you the longest freely swinging pendulum, leaving enough line to tie around the washers and clip into the bulldog clip.

3) Tie the washers together at one end of the line, such that they hang freely.

4) Clip the other end with the bulldog clip.

5) Blu-tack the bulldog clip to the top of your door frame (or tree branch etc.). You should now have a freely swinging pendulum. Ensure that the clip is clamped well to the frame and doesn’t move as your pendulum swings.

6) Using the tape measure, measure the length of your pendulum, from the point where the line is clipped to the middle of the washers.

7) Draw your pendulum back, keeping the fishing line taut, and then let it go, allowing it to swing freely. After letting the pendulum swing back and forth a few times to steady itself, measure how long it takes to do ten swings.

8) Repeat your measurement 10 times, recording the time after every measurement. Swap with your partner so that they can do the experiment too. Find the average time for one complete swing of the pendulum.

Use the equation above right to calculate little g.

9) If this method isn’t practical for you to do at home have a word with your science teacher to see if you can do this in school. They may have different apparatus that you can use. They can also help you use the equation to calculate little g (if you an A level physics student you should be able to do this experiment on your own).

10) When you have a value of little g that you are happy with/you have had checked then email Dr Sian Owen your value using the following email address schools.liaison@physics.ox.ac.uk Make sure you give information about yourself and where you got the information about the practical from.