Simple Pendulum - Assignment Example

Measuring g using a simple pendulum Name Date Abstract The purpose of this lab experiment is to determine the force of gravity (g) using a simple pendulum. By use of this experiment, the period of the pendulum was timed and the values were recorded for all the ten different length variations of the string. Furthermore since timing has uncertainty, it was determined to avoid errors that will affect calculations. The data obtained was used in the formula T = 2π√L/g to determine g. According to the equation T is the pendulum period, L is the length of the pendulum string, while g is the gravity (Matthews, 2006). Introduction A pendulum is a mass that is suspended at the end of a string and it is free to swing. According to history it was known and used by Chinese and later on it was developed by Galileo around 1600 (Matthews, 2006). Galileo found out an important property that makes pendulum important in timekeeping that is, a pendulum period is independent on the amplitude of the swing, which means pendulum swings will take the same time even if the swing has decreased due to other conditions such as friction. He also found out that it can be used to measure acceleration due to gravity (Matthews, 2006). Experiments have shown that pendulum behaves exactly like simple harmonic motion. Simple harmonic motion is periodic movements whereby restoring force is equivalent to the displacement force. From a different point of view in simple harmonic motion displacement of an object changes often over time while following similar shape as cosine curve. But the velocity behaves differently, at maximum displacement the velocity is zero. The errors in this experiment come from precision in length of the string and time measurement apparatus, reaction time of stopwatch and its accuracy. The final result of the acceleration due to gravity (g) takes into account error correction using approximation method. When an object is dropped it will always moves toward the ground at the same rate irrespective of its weight, what is pulling the object towards the ground is called force of gravity. It means that when a heavy object and a light object are dropped from the same height they will land at the ground at the same time in condition that air resistance and wind does not interfere with; the rate in which objects drop to the ground from a certain height is called acceleration due to gravity. The pendulum was used to determine the acceleration due to gravity, the period of the pendulum depends on string length and g, a graph of L vs. T2 was drawn, and the graph slope should be g/4π2 (Matthews, 2006). Apparatus required Pendulum bob String Stand Meter ruler Stopwatch Lab stand Protractor G-clamp Diagram setup Figure 1: Apparatus set up Procedure To start with, a string of approximately 2 meters was tied to the bob. Then a ruler was placed in a vertical position to measure the length of 71 cm from the bob center of mass. The remaining part of the string was put in between the stand clamps and clamped The protector clipped to the top of the stand was used to determine the angle used of displacement before the bob is released to swing. When equipment setup was complete, the pendulum was displaced to approximately 10 degrees from the vertical and it was released to swing; the displacement should be small to minimize error when determining g using T = 2π√l/g. The moment the bob was released to swing the stop watch was started. The time taken by the pendulum to make 10 swings was recorded, the reason why 10 oscillations was used was meant to assist in minimizing errors that arises from reaction time when starting and stopping the timer. The same procedure was repeated using different lengths of the string. Potential health and safety issues When large masses are used they can damage the floor when they fall or injure the person performing the experiment legs if he is not wearing shoes. To avoid this, something should be placed on the lab floor to avoid the masses damaging the floor in case of a fall. Students should always wear the right clothing when in the lab, for example they should always wear shoes that cover the whole legs and not open shoes. Large amplitudes with large masses can injure the student face. To avoid this small amplitude should be used. Results Length, L (m) Time, t (s) Period, T (s) T2 (s2) 0.71 16.905 1.600 2.650 0.58 15.450 1.545 2.387 0.54 14.545 1.450 2.103 0.45 13.735 1.370 1.877 0.36 12.265 1.220 1.488 0.28 10.800 1.075 1.156 0.21 9.650 0.960 0.922 0.16 8.740 0.870 0.757 0.10 6.490 0.645 0.416 The graph obtained from the data above is shown below. Figure 2: A graph of length, L, of the pendulum against period square, T2 Calculation After drawing the graph of L against the length T2, the gradient from the graph was used to calculate the value of g. From the equation the square root is removed by squaring both sides to obtain: , making L the subject of the formula, the formula becomes , since L α T2, then g/ 4π2 will be the gradient of the graph. To get the gradient of a graph we calculate by change in y axis divided by change in x axis, which is change in length L divided by change in T2 Thus, = 0.236m/s2 Making g the subject of the formula we get g = 0.236 m/s2 x 4π2 g = 9.324 m/s2 Percentage error from the experiment, = 5.02% Conclusion and evaluation The experiment was carried out properly as per the procedures and this assisted in minimizing the errors. The aim of the experiment was to find the acceleration due to gravity using the pendulum and compare it with theoretical value; the universal accepted theoretical value of g is 9.817 ms2 though at times it varies depending on places. The value we obtained from our experiment is 9.324 ms2; it is almost the same as theoretical value, this proves our hypothesis. There were nine data points with two trials for each. As the length of the string increases the time taken to make 10 oscillations also increases, for example for 10 cm length it took 6.49 second and for 71 cm length it took 16.9 seconds. The reason for this is that the velocity of the bob increases because it has to cover large distance in a long string. The percentage error from the experiment was found to be 5.02%, this shows that there were certain flows when conducting the experiment. The sources of errors in this experiment include air friction, innate variation in human reaction time in operating the timer, shaking of the stand during oscillation, lengthening of the sting during oscillation, imperfection when measuring the length of the string, rounding off numbers to small figures and parallax error. To minimize these errors, certain precautions need to be put in place. In every data point before measuring the time of oscillation for the second time the string should be measured first if it is still the right length (An OER from Textbook Equity, 2014). The stand should be always kept stationary; this can be done by putting extra weight on the bottom of the stand. The innate variation resulting from human timing can be reduced by increasing the number of oscillation to 20. In calculations, up to four decimal numbers should be used, this will minimize calculation errors. To further improve on this experiment, it should be carried out in a more sophisticated way to improve its accuracy. Light gates should be used because it can remove the error resulting from reaction time because it will accurately time the moment a bob complete its oscillation (An OER from Textbook Equity, 2014). The affect resulting from air resistance can be investigated by changing pendulum displacement. In conclusion, the experiment was successful because we managed to achieve its objective of measuring the acceleration due to gravity by use of a pendulum; we also managed to compare it with the accepted value. The experimental value was 9.324 while the accepted value is 9.817; the difference is as a result of errors encountered while carrying out the experiment. References An OER from Textbook Equity (2014). College physics textbook equity edition volume 2 of 3: Chapters 13 - 24. United Kingdom: Lulu.com. Chen, Y. T., & Cook, A. H. (2005). Gravitational experiments in the laboratory. Cambridge, Cambridge University Press. Matthews, C.G.F. (2006). The pendulum: Scientific, historical, philosophical and educational perspectives. Edited by Michael R. Matthews, Colin F. Gauld, and Arthur Stinner. United States: Springer-Verlag New York. Draft Measuring g using a simple pendulum Name Date Abstract The purpose of this lab experiment is to determine the force of gravity (g) using a simple pendulum. By use of this experiment, the period of the pendulum was timed and the values were recorded for all the ten different length variations of the string. Furthermore since timing has uncertainty, it was determined to avoid errors that will affect calculations. The data obtained was used in the formula T = 2π√L/g to determine g. According to the equation T is the pendulum period, L is the length of the pendulum string, while g is the gravity (Matthews, 2006). Introduction A pendulum is a mass that is suspended at the end of a string and it is free to swing. Accordingto history it was known and used by Chinese and later on it was developed by Galileo around 1600(Matthews, 2006). Galileo found out an important property that makes pendulum important in timekeepingthat is, a pendulum period is independent on the amplitude of the swing, which means pendulum swings willtake the same time even if the swing has decreased due to other conditions such as friction. He also foundout that it can be used to measure acceleration due to gravity (Matthews, 2006). Experiments have shownthat pendulum behaves exactly like simple harmonic motion. Simple harmonic motion is periodicmovements whereby restoring force is equivalent to the displacement force. From a different point of view in simple harmonic motion displacement of an object changes often over time while following similar shape as cosine curve. But the velocity behaves differently, at maximum displacement the velocity is zero. The errors in this experiment come from precision in length of the string and time measurement apparatus, reaction time of stopwatch and its accuracy. The final result of the acceleration due to gravity (g) takes into account error correction using approximation method. When an object is dropped it will always moves toward the ground at the same rate irrespective of its weight, what is pulling the object towards the ground is called force of gravity. It means that when a heavy object and a light object are dropped from the same height they will land at the ground at the same time in condition that air resistance and wind does not interfere with; the rate in which objects drop to the ground from a certain height is called acceleration due to gravity. The pendulum was used to determine the acceleration due to gravity, the period of the pendulum depends on string length and g, a graph of L vs. T2 was drawn, and the graph slope should be g/4π2 (Matthews, 2006). Apparatus required Pendulum bob String Stand Meter ruler Stopwatch Lab stand Protractor G-clamp Diagram setup Figure 1: Apparatus set up Procedure ? To start with, a string of approximately 2 meters Measuring g using a simple pendulum Name Date Abstract The purpose of this lab experiment is to determine the force of gravity (g) using a simple pendulum. By use of this experiment, the period of the pendulum was timed and the values were recorded for all the ten different length variations of the string. Furthermore since timing has uncertainty, it was determined to avoid errors that will affect calculations. The data obtained was used in the formula T = 2π√L/g to determine g. According to the equation T is the pendulum period, L is the length of the pendulum string, while g is the gravity (Matthews, 2006). Introduction A pendulum is a mass that is suspended at the end of a string and it is free to swing. According to history it was known and used by Chinese and later on it was developed by Galileo around 1600 (Matthews, 2006). Galileo found out an important property that makes pendulum important in timekeeping that is, a pendulum period is independent on the amplitude of the swing, which means pendulum swings will take the same time even if the swing has decreased due to other conditions such as friction. He also found out that it can be used to measure acceleration due to gravity (Matthews, 2006). Experiments have shown that pendulum behaves exactly like simple harmonic motion. Simple harmonic motion is periodic movements whereby restoring force is equivalent to the displacement force. From a different point of view in simple harmonic motion displacement of an object changes often over time while following similar shape as cosine curve. But the velocity behaves differently, at maximum displacement the velocity is zero. The errors in this experiment come from precision in length of the string and time measurement apparatus, reaction time of stopwatch and its accuracy. The final result of the acceleration due to gravity (g) takes into account error correction using approximation method. When an object is dropped it will always moves toward the ground at the same rate irrespective of its weight, what is pulling the object towards the ground is called force of gravity. It means that when a heavy object and a light object are dropped from the same height they will land at the ground at the same time in condition that air resistance and wind does not interfere with; the rate in which objects drop to the ground from a certain height is called acceleration due to gravity. The pendulum was used to determine the acceleration due to gravity, the period of the pendulum depends on string length and g, a graph of L vs. T2 was drawn, and the graph slope should be g/4π2 (Matthews, 2006). Apparatus required Pendulum bob String Stand Meter ruler Stopwatch Lab stand Protractor G-clamp Diagram setup Figure 1: Apparatus set up Procedure ? To start with, a string of approximately 2 meters Read More