Scientific Report - Pendulum Motion

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  • Topic: Pendulum, Measurement, General relativity
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  • Published : December 11, 2011
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HSC PHYSICS
2011
HSC PHYSICS
2011

PENDULUM MOTION
BY NATHAN LOCKE

Image taken from http://www.practicalphysics.org/go/Experiment_480.html Pendulum Motion
Aim: To determine the rate of acceleration due to gravity by using a pendulum. Background Information:
Equation One:
T=2πlg
Where
T = the period of the pendulum (s). This is the time taken for the pendulum to return to its starting position. l = length of the pendulum
g = the rate of acceleration due to gravity (ms-2)
* In order to find the acceleration due to gravity, the equation must be rearranged to look like this, and give “g” as the subject: g=4π2lT2
Procedure:
1. Mass to stop the stand falling over
Mass to stop the stand falling over
Protractor (attached)
Protractor (attached)
Bosshead
Bosshead
Retort Stand
Retort Stand
Mass
Mass
String
String
Clamp
Clamp
In a group of 2, we set up the apparatus shown below:

2. We measured the length of the pendulum from the base of the mass to the swinging point on the clamp. We recorded this length in our table. 3. We moved the position of the pendulum to 27° from the vertical. 4. We released the pendulum, and recorded the time taken for ten complete oscillations using a stopwatch. 5. We reduced the length of the pendulum by approximately 8cm and repeated steps two to five, six times. 6. We individually plotted a graph of Length versus Period2. 7. We then completed the remaining sections of the investigation.

Controlling our variables
* We kept the position of the protractor constant. This allowed us to get the same reading for the angle from the same position every time. * We measured the pendulum from the same point each time, to keep our measurements consistent. * We used the same mass for all tests.

* We kept the string tight when we dropped the mass, so it wouldn’t bounce and alter the “swing.” * We kept the same jobs ie. The same person timed, dropped, adjusted the string etc.

Results
Length (m)| Time for ten (s)| Period (s)| Period2 (s)| 1.000| 20.37| 2.04| 4.16|
0.930| 19.43| 1.94| 3.76|
0.850| 18.25| 1.83| 3.35|
0.770| 17.69| 1.77| 3.13|
0.690| 16.62| 1.66| 2.76|
0.620| 15.75| 1.58| 2.49|
0.560| 15.00| 1.50| 2.25|

Analysis Of Results
1. The gradient of our graph was:

m= y2-y1x2-x1 = 1-0.564.16-2.25=0.23

2. In order for “g” to be the gradient of our graph, the y-axis had to be changed to “4π2l”, or the final gradient value needed to be multiplied by 4π2. 3. The rate of acceleration due to gravity for our experiment:

g=4π21.004.16=9.49 ms-2 g=4π20.933.76=9.76 ms2 g=4π20.853.35=10.02ms2

This left an average value for the acceleration due to gravity, as 9.76ms2.

Discussion Questions
This investigation was best conducted in a team, as it required lots of things to be done at once. The mass had to be dropped at the right angle, the timer started, and the timer stopped at the same position as it started from, and the mass had to be dropped parallel to the bench top, so it wouldn’t hit the bench. Although there are benefits of conducting this experiment in teams, this experiment could be better conducted as an individual. The timer had to start the instant that the mass was dropped, as to get an accurate reading, and if the one person was to do both of these things, it would be much easier to achieve this result.

There was quite a large margin of error in this experiment, as there was many variables. The angle of drop, the tension of the string and the positions that time was taken at could all change the result of this experiment, and are all quite hard to measure perfectly with the basic lab equipment that was used. Although there was a lot of room for error, these errors were kept reasonably constant, as the drop might have been out by a few degrees each time, or...
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