Gravitational Boost due to Ordinary Pendulum - Research Paper Example

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 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 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 4π2/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. i. 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. ii. The blocks were put together with the string between the two blocks and they were squeezed together using the clamps jaws. iii. The mass object was tied on the other end of the string; the mass should be in a position of swinging freely. iv. 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. v. 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 formula (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. vi. The experiment was repeated without changing any measurement; the average of the readings was recorded. This was done to eradicate anomalous results. vii. Step five and six was repeated eight times with different lengths of the string in every measure setup. viii. 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 on L. From the equation of the period of pendulum when both sides of the equation are squared, we get T2= L4π2/g. the general equation of a straight line is given by y= m x + c where m stand for the straight line gradient (Psillos & Niedderer, 2002). C is 0 for the line that goes through the origin; this graph line goes through the origin (0, 0). Substituting the terms of the pendulum equation into y=m x + c, we get T2= L4π2/g, whereby y=T2, X= L, and m is the gradient of the line which is 4π2/g. The gradient of a line is calculated by the equation = = = 0.263 ms2. Graph gradient is equated with m, 0.263 ms2= g= 39.49 x 0.263= 10.39 ms2 The experimental value of g is not far from the accepted value which is 9.8ms2 The difference is caused by errors encountered while carrying out the experiment. To calculate the percentage error% the formula, is employed. = % Discussion and Conclusion The experiment was successful because we managed to find the value of g using a pendulum and we managed to compare it with the accepted value. The value of g obtained from the experiment is 10 ms2 while the accepted value is 9.8 ms2. The difference between the accepted value and experimental value is due to the errors that affected the measurements. I encountered certain difficulties while performing the experiment this includes measuring the exact length of the string and starting the stopwatch the moment I released the mass to swing. The other problems that affected the experiment were air friction. The experiment was improved by improving the reliability of the procedure given. The air resistance error can be reduced by increasing the displacement and repeating the same set of data more than two times. The exact length can be improved by measuring the string after completion of the 10 oscillations for the same set of data. A tall object can be placed behind the pendulum to serve as a fiducial marker. The stopwatch will be put on and off once the pendulum passes the marker, this will reduce parallax error in charging where the pendulum is. Bibliography Muncaster, R. (2003). A-level physics. Cheltenham, Thornes An OER from Textbook Equity (2014) College physics textbook equity edition volume 2 of 3: Chapters 13 - 24. United Kingdom: Lulu.com. Psillos, D., & Niedderer, H. (2002). Teaching and learning in the science laboratory. Dordrecht, Kluwer Academic Publishers Read More