TheoryIf an object is dropped, it will fall at the same rate irrespective of how heavy it is. This implies that if a heavy object and a light object are dropped from the same height they will always land at the same time (if the effect of air resistance or wind is assumed). The rate at which objects fall from a given height to the surface of the Earth is referred to as the acceleration due to gravity, g. In this case, we will use a simple pendulum to obtain the value for g.
The period T, or the time of the pendulums swing, depends on the length of the string and the acceleration resulting from the gravity, g. Where T, is the time taken for one complete oscillation or swing, L, is the length of the pendulum. By varying the length, L, of the pendulum and measuring the corresponding T, time period it is possible to calculate the acceleration due to gravity, g. You will need to manipulate the equation in order to determine the data you will have to plot on a graph. ProcedureA pendulum bob was suspended from between two blocks of wood that was held in a clamp attached to the clamp stand so that the pendulum length from the point of suspension to the centre of the bob is 30cm. The pendulum was displaced by less than 10o from the vertical and set it into simple harmonic motion. Time taken for the pendulum for 10 swings was then measured. The procedure was repeated for the varying lengths of pendulum. The data obtained was then used to calculate the acceleration due to gravity, g.Results and calculationsLength of Pendulum L (cm)- independent VariableTime for 10 swings (10) in (s)- Dependent VariablesTime period T (s)5014.561.45013.8851.38854712.381.2384713.031.3034012.871.28740131.33712.381.2383712.301.233011.901.193011.601.162711.471.142711.801.18209.500.95209.560.956178.310.83178.880.88107.40.74107.50.7575.940.5976.160.61Length of Pendulum L (m)- independent VariableMean time period (s)Time period2 (s2)g= 39.44L/T20.51.3941.94 10.160.471.2711.62 11.440.41.2941.67 9.4360.371.2341.52 7.7720.31.1751.38 8.570271.161.35 7.9230.20.9530.91 8.6920.170.860.74 9.0720.10.7450.56 7.1070.070.6050.37 7.551A graph showing Time Period2/s2 against Length of Pendulum/ mDiscussionThe results obtained were very interesting since the results exhibit simplicity.
The only things that affected the period of a simple pendulum were the length and the acceleration because of gravity. The period was completely dependent on the factors like mass.
When the length of the pendulum is precisely, like it was known in the experiment, it can actually be used to measure the acceleration due to gravity. When the angle is less that approximately 15o, the period T for a pendulum is nearly independent of amplitude, as with simple harmonic oscillators. For those amplitudes that are more than 15o the period increases gradually with the amplitude. The period increases asymptotically to infinity as the angle approaches 180o is an unstable equilibrium point for the pendulum (Aggarwal, Verma and Arun. , 2005, 35).
The only exception that Gravity exerts a force on every object that is exposed to it. The force of gravity is proportional to the mass of the object it is exerting that force on. A constant of the proportionality refers to the acceleration of gravity (g). The gravity acceleration (g) decreases with the increasing elevation; however, for a few thousand feet above the Earth’s surface, it remains fairly constant. ConclusionThe acceleration gravity of the pendulum at different lengths was as shown in the table below.