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IB Lab Measuring g with a Pendulum Model Answer

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Introduction

IB Lab – Measuring ‘g’ with a Pendulum – Model Answer

Results

Length/m ± 0.01

Time for 10 oscillations/s ± 0.4

Period/s ± 0.04

Period Squared / s2

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Middle

0.2

1.00

20.3

2.03

4.1

0.2

1.10

21.0

2.10

4.4

0.2

1.20

22.2

2.22

4.9

0.2

1.30

23.0

2.30

5.3

0.2

Data Processing

To find the uncertainty in period squared, there are (at least) two equally acceptable methods:

First Method

Double the relative uncertainty for period, using the equation:

image00.png

e.g. for l = 0.100 ± 0.005 m, T = 0.69 ± 0.04 s:

∆(T2) = 0.48 x 2 x 0.04/0.69 = 0.055652≈ 0.06 (to 1 sig. fig.)

Second Method

Find the maximum and minimum values of period squared, take the difference and divide by two.

e.g. for l = 0.100 ± 0.005 m, T = 0.69 ± 0.04 s:

T2 = 0.692 = 0.4761

Tmax = (0.69 + 0.04)2 = 0.5329

Tmin = (0.69 – 0.04)2 = 0.4225

So ∆(T2) = (0.

...read more.

Conclusion

The first few oscillations were quite erratic, which may have affected the period

Possible improvements to the procedure would be:

  • Use data-logging apparatus (e.g. Acquire datalogger and motion sensor) to record the motion of the mass
  • Use a larger range of lengths of string, to reduce the relative uncertainty in the length
  • Measure the time for 50 oscillations instead of 10, to reduce the relative uncertainty in the period
  • Mark clearly the centre of mass of the object
  • Allow the mass to oscillate a few times before starting measurements

image08.png

...read more.

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