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Pendulum Motion

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Introduction

Physics Design Lab

Pendulum Motion


PURPOSE:

To determine the relationship between the period of a pendulum and various factors, assessed individually, which are the mass of the pendulum, length of the attached string, and angle of release.

THEORY AND HYPOTHESIS:

Many factors affect the swinging motion of a pendulum. My design lab intends to reach a conclusion on the factors that do, and do not, affect the motion of a pendulum. I hypothesize that the mass of the pendulum will not affect the period because the acceleration of gravity is the same for all masses on Earth. The length of the string will affect the period because it affects the distance that the pendulum travels. The angle of release should also affect the period because it also changes the distance the pendulum travels in a period.

MATERIALS:

  • ruler
  • string cotton
  • pen
  • masking tape
  • ring stand
  • ring clamp
  • weights (15g, 20g, 60g, 100g, 200g, 500g)
  • centigram balance
  • protractor
  • stopwatch

PROCEDURE:

Part 1 - Set-up

  1. Gather all materials.
  2. Tidy and clean lab table.

Part 2- Mass

  1. Attach ring clamp to ring stand.
  2. Cut a piece of string noticeably longer than 30cm.
  3. Tie the 15g weight to the string.
  4. Adjust the string such that the weight is 30cm from the ring.
  5. Secure string to the ring clamp with tape and hand.
  6. Make sure the pendulum is horizontal (180 degrees to the horizon)
...read more.

Middle

Length l (cm)

Period T (s)

Average period Tavg (s)

10 ±3

0.88±0.5

0.88±0.5

0.81±0.5

0.84±0.5

0.85±0.5

0.85±0.5

20 ±3

1.13±0.5

1.16±0.5

1.16±0.5

1.12±0.5

1.12±0.5

1.14±0.5

30 ±3

1.35±0.5

1.35±0.5

1.31±0.5

1.35±0.5

1.32±0.5

1.34±0.5

40 ±3

1.50±0.5

1.50±0.5

1.47±0.5

1.50±0.5

1.47±0.5

1.49±0.5

50 ±3

1.72±0.5

1.68±0.5

1.75±0.5

1.65±0.5

1.69±0.5

1.70±0.5

Table 3 – The affect of angles on period

(Note: mass of weight is 100g; length of rope is 30 cm)

Angles a (degrees °)

Period T (s)

Average period Tavg (s)

180±5

1.34±0.5

1.34±0.5

1.37±0.5

1.31±0.5

1.31±0.5

1.33±0.5

195±5

1.25±0.5

1.22±0.5

1.21±0.5

1.23±0.5

1.25±0.5

1.23±0.5

210±5

1.15±0.5

1.21±0.5

1.22±0.5

1.16±0.5

1.16±0.5

1.18±0.5

225±5

1.16±0.5

1.13±0.5

1.13±0.5

1.15±0.5

1.13±0.5

1.14±0.5

240±5

1.12±0.5

1.13±0.5

1.06±0.5

1.09±0.5

1.10±0.5

1.11±0.5

255±5

0.97±0.5

1.00±0.5

1.06±0.5

0.97±0.5

1.00±0.5

1.00±0.5


OBSERVATIONS:

Graph 1, 2, 3, and 4 attached.

...read more.

Conclusion

-4 s/g (m) + 0s) represents the length of the period as a function of the mass; as we can see from the equation, the mass will not have a significant impact on the period of the pendulum motion.

There is no accepted value for this design lab; therefore, it is inappropriate to designate an arbitrary value to compare to my measured value.

SOURCES OF UNCERTAINTY:

  • human error (timing, angles, length of string)
  • timing – ±0.5s (biggest difference out of 5 values)
  • angles - ±5° (protractor was accurate but it was sometimes hard to read)
  • length of string - ±3cm (we measured the specified length of string before taping and tying the rope, creating room for error)
  • air resistance
  • negligible, but clearly relevant in Graph 1 and Graph 2
  • friction in the ring clamp
  • the curved shape of the clamp
  • I chose to record each period separately as opposed to dividing a total number of periods by its swings because I believe that he extra swings would bring in many unknown factors into the system such as momentum. By recording each swing separately, I can make sure that each swing is clean and the weights will not sway or jump. However, multiple timings can create more room for error; therefore I made up for the lost accuracy by increasing my uncertainty in timing.

...read more.

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