Laboratory report – First Draft
Determine the acceleration due to gravity using a simple pendulum
Objective
The objective of this practical is to determine acceleration due to gravity ‘g’ using the simple pendulum model. This is shown when a period of oscillation is seen to be independent of the mass of the mass ‘m’.
Theory
A simple pendulum consists of a mass that is attached to a string of length ‘L’ that is fixed to a point, in this case, a cork suspended by a clamp stand. This allows the mass to be suspended vertically downwards and allows it to be displayed at an angle that it swings. A period ‘T’ of oscillation is the time required for one complete swing. For this to happen ideally its mass must swing from an angle that is
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(Eg. 13.26/10 = 1.326)
Step 7: Now square each ‘T’ value to make ‘T^2’ (Eg. 1.3262 = 1.758)
Step 8: We can now plot our values into the rearranged equation to figure out acceleration due to gravity ‘g’. (Eg. (4π2 x 43.70)/ 1.758 = 981.4 cm/s2)
Step 9: Because we measured the lengths in centimeters rather than meters, we need to calculate are ‘g’ value into m/s2 so we can compare it to the SI unit for acceleration due to gravity. (Eg. 981.4/100 = 9.81 m/s2)
Step 10: Draw a scatter plot of T2 on the Y-axis against L on the X-axis.
Results
Length (cm)
1
(s)
2
(s)
3
(s)
Mean
Time (s)
T
(Time/10)
T2
g (cm/s2) g (m/s2)
43.70
13.16
13.35
13.28 13.26 1.326 1.758 981.4 9.81
37.50
12.07
11.90
12.06 12.01 1.201 1.442 1026 10.27
33.10
11.41
11.28
11.31 11.33 1.133 1.284 1018 10.18
27.30
10.53 10.63 10.44 10.53 1.053 1.109 972 9.72
22.20
9.350 9.250 9.440 9.350 0.935 0.874 1003 10.03
17.00
8.440
8.280
8.220 8.310 0.831 0.691 971 9.71
11.80
6.880 7.000 6.910
6.930
0.693 0.480 971 9.71
Discussion and Conclusion
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