Dear Students,
Kindly work out and submit the following question on Data Analysis by Friday 24th April, 2015. You are encouraged to do your best in attempting all subsequent questions as allotted marks will form part of your third assessment.
Good luck,
Crisby
Question:
A light spring of unstretched length 2.2cm is suspended from a clamp as shown. The pointer indicates 28.4cm on the ruler.
(a) A 20-g mass is attached to the spring, which extends. Calculate the extension if the pointer now indicates 27.0cm.
The spring is now displaced vertically and allowed to oscillate. The time for 20 oscillations is measured by means of a stopwatch. The experiment is repeated, each time increasing the mass by 20g, and timing 20 oscillations. The readings are tabulated below.
Mass (g) | Ruler reading (cm) | Initial extension, e (cm) | Time for 20 oscillations (s) | T (s) | T^{2} (s^{2}) |
0 | 28.4 | — | — | — | — |
20 | 27.0 | 4.7 | |||
40 | 25.6 | 6.7 | |||
60 | 24.2 | 8.2 | |||
80 | 22.8 | 9.5 | |||
100 | 21.4 | 10.6 |
(b) Work out the extension e (cm) and the periodic time T (s) in each case, and complete the table.
(c) Plot the values of T^{2} (y-axis) against e (x-axis), and draw the best straight line through your points.
(d) Measure the gradient of your graph.
(e) The period of oscillation of such a spring is related to the initial extension by the equation:
T = 2π√(e/g)
Use your graph to determine a value for g, the acceleration due to gravity.
(f) Suggest two ways in which the experiment might be improved in order to give a more accurate result.
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