Determining gravity acceleration using a simple pendulum (Lab Report Sample)

Determining gravity acceleration using a simple pendulum Student name Course Tutors name School Department Date Introduction In this experiment the time of 10 oscillations of different lengths of a string attached to the suspended mass was measured, the angle in which the pendulum was left to swing was kept constant. For different lengths and fixed angle, evidence of a linear relationship between period T2 and length L is observed. By drawing a graph using the values of T2 and L and using the formula T=2Ï€L/g we found that the acceleration due to gravity is 10.39 ms2. In nature several things wiggle in periodic fashion, in other words they vibrate. An example of such thing is a simple pendulum. The movement of the pendulum suspended material represents period motion that was used long time to measure time (Muncaster, 2003). Such kind of oscillatory motion is known as simple harmonic motion. Well known scientist Galileo was the first person to observe that the time taken by a simple pendulum to swing to and fro over a certain distance depends only on the length of the string that is attached to the mass (Muncaster, 2003). The time it takes to complete one oscillation does not depend on the suspended mass or the angle to the vertical in which the mass is released. Acceleration due to gravity is involved in the oscillation of the mass; the universal accepted g is 9.8 ms2. For over a long period of time, acceleration due to gravity has been known to be constant irrespective of the mass of the object (An OER from Textbook Equity, 2014). In a situation where there is no air resistance for example in a vacuum two different objects of different masses for example a paper and cannonball when released from the same height they will hit the ground at the same time. In this experiment we shall measure the force of gravity g using a simple pendulum. A simple pendulum is a simple experiment that can be easily performed in a lab by students. It is made up of a mass m suspended using a string of a certain length. It is then suspended using a stand; the mass is the released with an angle to the vertical and the mass will then make oscillation in a plane. The relation between the length and the period is given by the formula T=2Ï€L/g whereby T is the period of oscillation, g is the gravitational force, and L is the length of the string (Psillos & Niedderer, 2002). From the formula it implies that T2 should be proportional to L and constant of proportionality is 4Ï€2/g. When several measurements of T2 are graphed with different values of L we shall be in a position of experimentally determining the constant of proportionality and acceleration due to gravity g. Apparatus used The apparatus used in the experiment include Stopwatch A ruler Metal washers (mass to be suspended) Ring stand or other support for clamp One meter string Clamps Two small pieces of wood that can be closed in the jaws of the clamp Protractor Apparatus setup diagram. Method used. * The clamp was attached to the ring stand so that it can freely hold the string. The mass suspension should be friction free so that wood blocks are the used to provide string suspension. * The blocks were put together with the string between the two blocks and they were squeezed together using the clamps jaws. * The mass object was tied on the other end of the string; the mass should be in a position of swinging freely. * The length of the string is measured from where it is leaving the wooden blocks to the middle of the suspended mass. The length is the recorded in the table for the first data set. * The pendulum was pulled away from the vertical to an angle of 10 degrees, the protractor was used to measure this angle, when it is exactly 10 degrees allow it to swing, the moment it is allowed to swing the stopwatch was started. How long it takes to make 10 complete swings was measured and recorded. The displacement should be large, mainly from 10 degrees and above this will reduce the error while calculating g using the formulaT=2Ï€L/g (Psillos & Niedderer, 2002). Using several complete oscillations is advisable because it minimizes the errors that arise due to reaction time when starting and stopping the timer. * The experiment was repeated without changing any measurement; the average of the readings was recorded. This was done to eradicate anomalous results. * Step five and six was repeated eight times with different lengths of the string in every measure setup. * To find the period T, the time value for the 10 swings was divided by 10. Potential health and safety issues Injuries on the legs resulting from falling stands from the table, some stands are heavy and if they fall from the table to the ground they can injure student's legs if they are wearing open shoes or sleepers. To deal with this problem student should always wear closed shoes in the lab while carrying out their experiments. Furthermore stands can be fixed on the table to prevent them from falling. Results Length, L (m) Time, t (s) Average time (s) Period, T (s) Average period (s) T2 (s2) 0.71 16.90 16.91 16.905 1.69 1.69 1.600 2.650 0.58 15.50 15.40 15.450 1.55 1.54 1.545 2.387 0.54 14.91 14.18 14.545 1.49 1.41 1.450 2.103 0.45 13.72 13.75 13.735 1.37 1.37 1.370 1.877 0.36 12.28 12.25 12.265 1.22 1.22 1.220 1.488 0.28 10.75 10.85 10.800 1.07 1.08 1.075 1.156 0.21 9.85 9.45 9.650 0.98 0.94 0.960 0.922 0.16 8.88 8.60 8.740 0.88 0.86 0.870 0.757 0.10 6.53 6.45 6.490 0.65 0.64 0.645 0.416 Results analysis The graph shows the dependence of T2 ...