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The Affect of Mass on the Period

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Introduction

Colin Wick                2/17/09

Period 4                IB Physics

The Affect of Mass on the Period

How does the mass affect the period of a pendulum?  We believe that if the mass of a pendulum were increased, then the period of the pendulum would decrease, because as the mass is increased so is the downward force of gravity acting on the pendulum, causing the acceleration of the pendulum to increase.  This experiment will be conducted by taping a “light”, measured string to a table so that it hangs 90 degrees to the horizontal.  Measured masses will then be attached to the string for each data point, and the resulting period recorded for five trials.  The gathered data will be graphed in order to visually represent the affect that mass has on the period of a pendulum.  The only variable that will be manipulated in this experiment will be the mass on the end of the pendulum, while the angle of release and the length of the string will remain same.  The angle of release and string length will be controlled, because by changing either of them, the distance the pendulum must travel is also changed.  Therefore, both controlled variables could conceivably affect the period of the pendulum.  If our hypothesis is correct, then the period of the pendulum will have an inverse response to the mass, meaning that as the mass increases, the period of the pendulum should decrease.

The materials utilized in our experiment are listed in bullets below and set up according to the following diagram: • Pre-measured 20 gram mass
• Pre-measured 50 gram mass
• Pre-measured 100 gram mass
• Pre-measured 200 gram mass
• Pre-measured 250 gram mass
• “Light” string (34cm)
• Meter stick to measure string
• Protractor
• Stopwatch
• Table
• Tape

Middle

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Uncertainty (±)

20.0

0.2

1.0

1.0

1.1

1.1

1.1

0.1

50.0

0.2

1.1

1.0

1.1

1.1

1.1

0.1

100.2

0.2

1.1

1.1

1.1

1.1

1.1

0.1

200.2

0.2

1.1

1.1

1.0

1.1

1.1

0.1

250.3

0.2

1.1

1.1

1.1

1.1

1.1

0.1

 Average Period (s) Average Period Uncertainty (±s) 1.06 0.16 1.08 0.18 1.10 0.10 1.08 0.18 1.10 0.10 This graph illustrates that there is no relationship between the mass and period of a pendulum because the slope of the graph is so close to zero.  Therefore, the period constantly stays exceptionally close 1.1s despite the change in mass.  The uncertainty in mass is not represented in the graph because it is so miniscule that it cannot be seen without misrepresenting data.

The calculations that were done in this lab are represented below through explanations and examples (all examples use data from data point three), as well as the various uncertainties used.

Uncertainty of Mass:

Conclusion

There are a number of improvements that could be made to the lab that would decrease, and in some cases eliminate both the systematic and random error that was encountered.  The first improvement would almost entirely eliminate the systematic error of air friction by conducting the trials inside a vacuum.  By eliminating air friction, we would make the surface area of the masses obsolete.  The second enhancement to the lab that would make the gathered data more reliable, would be to instead of tape the pendulum to the table, to tie it to a bar bridging two tables.  Therefore, the bar would be able to hold the added mass successfully, unlike the tape, allowing us to gather data without having to occasionally reset the lab, lessening the chance that the string length would change.  Finally, we could set up an infrared timing system where a beam would be aimed at the top of the pendulums swing on one side and when allowed to connect would start time (the mass would be in the way at the start), and when broken again (when the mass has completed one period) would stop time.  This would make the collection of time much more accurate, eliminating the human error of pressing the start and stop button on the timer at exact moments.

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