Apparatus needed:
- A long piece of string about 10 m.
- A mass (loads) or a ball.
- Stopwatch
- Clipboard, pencil and paper.
- A metal bar.
- A retort stand
- Meter rule
Method of experiment:
- Find an area where there is a small playground which you can use to tie the string.
- Tie the string to the load or ball.
- Measure a certain length of the string and tie the string on the metal bar.
- Next to the string that you tied, tie another string at a small angle and hold the end of it with the retort stand so that it doesn’t move.
- Lift the string with the load on so that it matches the other string that you just tied i.e. so that they have the same angle. Use a spirit level or ruler to make sure that the two string are in line.
- Leave the load and time one oscillation (this means that it must go forward and come back to the original position).
- Now untie the string and use a longer piece of string. Repeat steps 3, 4, 5, 6 making sure that you are using the same ball and the same type of string.
- Again, when you timed one oscillation untie the string, get a longer piece and repeat step 3, 4, 5, 6. Do these as many times as you need.
Method of Collecting Data:
- First of all, if you have enough space, use a string with 50 cm intervals. In other words first measure the period with a 50 cm string, then with 1 m string, then with 1.5 m, etc.
- Instead of timing straight away, allow the load to swing about five times to get more accurate timing on start.
- Time 20 oscillations and then divide your answer by 20 in order to get a much more accurate result.
- Make people help you. Let one person leave the mass, and two other people start stopwatches in order to get more readings and hence more accurate results.
- Do about three trials for each length in order to calculate averages and get a much more accurate result.
- Write all your results in a table and then draw graph to see the correlation between T and L.
Data Collection and Processing
Data collection:
Table showing the Period for 20 oscillations obtained at different lengths. (All time readings to two decimal places).
We have two readings for each trial because we had to stopwatches going at the same time. Our next step is to find an average for each reading.
Table showing the Period for 20 oscillations obtained at different lengths. (All time readings to two decimal places).
Data processing:
Our next job is to actually find an average for the 20 oscillations and then find the time for 1 oscillation. To find the average for the 20 oscillations we will add the three trials for each length and divide them by 3. To find the average oscillation we will divide our answer by 20.
E.g. for 0.5m average for 20 oscillations →(29.94+29.92+29.90)/3=29.92
Average for 1 oscillation= 29.92/20= 1.50 (All results to two decimal places).
Table showing the average time for 20 oscillations and then the period.
Our final step is to find the constant in order to then find g. But before we can do that we have to square T. When T is squared we find the constant by dividing T by L. When the constant is found we divide 4π2 by constant to find g.
E.g. for 0,5m →T2=2.24→ K (constant)=T2/L=2.24/0.5= 4.48 therefore,
G=4π2/4.48= 8.82
Table showing the values of g obtained by our experiment.
Data presentation:
If we draw a graph with T2 on the y-axis and L on the x-axis we may see a linear correlation.
From the graph we can see that the gradient of the line is 3.9931. This is equal to the constant. In order to find g we will divide the gradient by 4π2.
Conclusion and Evaluation
Conclusion: In essence, we can conclude that our results aren’t very close to the known gravitational field strength of the earth. In fact we can calculate the percentage error for each one by finding the difference between our value and the theoretical value, then dividing by the theoretical value and multiplying by 100.
For 0.5m → (9.81-8.82)/9.81*100=10.1%
For 1.0m → (9.81-9.24)/9.81*100=5.81%
For 1.5m → (9.81-9.52)/9.81*100=2.96%
For 2.0m → (9.81-9.58)/9.81*100=2.34%
We can see that our error for some reason has decreased as the length of the string increased. However, despite that we cannot neglect the fact that there were many random and systematic errors that made our results a little bit in accurate. Random errors such as reaction time in the stopwatch, reading of the rulers may have been inaccurate, keeping the angle the same was very hard and we might have had a parallax error when trying to keep the two strings parallel to each other. Furthermore, systematic error could have occurred with the stopwatches. Also the wind could have affected the period as the bob- at times- wasn’t suspending symmetrically.
Nevertheless, it is very interesting to look at the graph that we produced because even though our results are inaccurate when looking at the table, the graph gave a very close answer. This is true because the graph doesn’t look at one set of results but plots them all and then draws a line of best fit. After finding the gradient we found that g= 9.88ms-1. If we calculate the percentage error we get:
(9.89-9.81)/9.81*100=0.82%
This illustrates that the value for g that we got is in fact very close to the theoretical value of it when looking at the graph. As a result, this supports my prediction that it is possible to verify the gravitational field strength at Istra.
Evaluation: There were several weaknesses in our experiment. First of all, it was very hard to keep the angle the same all the time. This may affect the readings because it can affect the period. Also, it was hard to keep the bob moving symmetrically which again affects the period of an oscillation. Finally, it was hard to make sure that both people with the stopwatch started at the same time and therefore this distorted our readings for the period a little bit.
In terms of limitation, we couldn’t use a longer string because of the space and as a result our data may be insufficient to accurately show the earth’s gravitational field strength.
Improvements: Realistic improvements that could cut some weaknesses of the procedure could include using greater lengths of string and doing the procedure in a greater space. This would help to get more results and hence get an even closer answer to g. Moreover, I believe the more trials done, the better chance you will get of obtaining the best average value: perhaps 10 trials would be a good idea. Finally, we could use technology to get precise timing. It is possible to set a beam of light with a sensor that starts the stopwatch every time the bob cuts the beam and stops the stopwatch when the bob cuts the beam on the way back. That way we can get an exact value for the period.