Gravity On Earth Lab Report

1-a)Introduction For this lab we are trying to verify that gravity on earth is 9.81 m⁄s^2 , by using a simple pendulum. A simple pendulum consists of a string that is attached to a weight at one end and to a pivot from the other end, so when the string is swung this would be a pendulum. A pendulum is considered to be a simple harmonic motion. A simple harmonic motion is the restoring force that is experienced by the movement of an object from equilibrium to a distance and then back to equilibrium. The properties for the simple pendulum would be the period, length of the string which the weight is attached to and the amplitude. The period is depended upon the length of the rope and it affects the period. b) Objective The purposes of this experiment are: (1) to study the motion of a simple pendulum, (2) to study simple harmonic motion, (3) to learn the definitions of period, and amplitude, (4) to learn the relationships between the period, amplitude and length of a simple pendulum. Also to design an experiment to investigate the dependence of period on the mass, amplitude, and length of the pendulum. We can also determine the acceleration due to gravity using the theory, results, and analysis of this experiment. 2-Theory a) Brief Theoretical Background A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. A simple pendulum can be approximated by a small metal sphere which has a small radius and a large mass when compared relatively to the length and mass of the light string from which it is suspended. If a pendulum is set in motion so that is swings back and forth, its motion will be periodic. The time that it takes to make one complete oscillation is defined as the period T. The maximum distance that the mass is displaced from its equilibrium position is defined as the amplitude of the oscillation. We can get T(period) by two ways, in lab we will do it by experimental way, and the other way is for home, theoretical way, in which we will this formula. T =2 π √ ❑, where L is length of pendulum, g is acceleration of free fall. b) Equations The only equation is this, in this experiment.T =2 π √ ❑, where L is length of pendulum, g is acceleration of free fall. c) Diagrams 3- Experiment a) List of Equipment Retort stand, pendulum bob, string, metre rule, stopwatch. b) Experimental Diagrams c) Procedure In this lab we used our own design, we planned together to perform experiment. No specific procedure. Every part has its own procedure, so I will write separately. Part 1- Dependence on Amplitude In part 1 we used metal ball as our bob and we set the pendulum first in the lab. Then we used our cell phones as stopwatch and calculated the time of oscillations. So we decided to take the times of 10 periods together and then we divided it with 10. So we got our single period time. We calculated amplitude by simply using a cm ruler and we pointed from the 5-10-15-20-25 amplitude, and we conclude that the amplitude is approximately correct every time. We changed amplitude for each trial and kept same the length and mass. Part 2- Dependence on mass In part 2 we used two different masses, one bob was metal, and other one was wooden bob. Both had different masses.But the length and amplitude was same, we made the length and amplitude same for both bobs. Then we did the same, we took two trials at same length and amplitude but the with two different masses, and we took the time, period of each trial. Part 3- Dependence on length In this part everything was same except the length. And then the same as other parts we used cell phones as stopwatch to measure the time, period. Part 4- Calculating T In this part we had to measure the Theoretical T, by using the given equation above. 4- Results a) Data Tables Table 1:Trial Length Amplitude Time with 10 Oscillations Period,T (sec) 1 81 5 17.40 1.74 2 81 10 18.25 1.83 3 81 15 18.45 1.85 4 81 20 17.65 1.77 5 81 25 17.72 1.77 Table 2:Trial Length Amplitude Wooden ball 10 Oscillations 1 56 15 2 56 20 Metal ball 10 Oscillations Wooden ball period Metal ball period 14.87 15.02 1.48 1.5 14.84 16.10 1.48 1.6 Table 3:Length = 81 Length = 56 Trial Amplitude 10 oscillations period(sec) 10 oscillations period(sec) 1 25 15.17 1.52 17.72 1.77 Part 4- Calculating T I will use the formula given to calculate; T =2 π √ ❑ ⇨ T =2(3.14) √ ❑ ⇨ T = 1.80s, when length is 81. T =2 π √ ❑ ⇨ T =2(3.14) √ ❑ ⇨ T = 1.50s, when length is 56. b) Graphs Graphs are on the back of the lab report. c) Error calculation, Accuracy In this lab, main factor for errors is friction and air resistance. These two factors causes some of the changes from the actual results. One more factor is also possible to cause errors which is stopwatch, we should use photo sensors instead of using cellphones as stopwatches. Photo sensors will give more accurate and precise results. Also if there is any other way to measure the amplitude more precisely and accurately that will be much better. 5- Discussion of Results a) Possible sources of Error There are many sources for errors in this experiment. The biggest is the inaccurate timing of the periods. There is great random error by having a person starting and stopping the timer. This could be solved by using a photo-timer to accurately measure the periods. Also, there is random error in the measurement of L, as there was no center of mass marked on the mass, and the meter stick was being leisurely held in place to eyeball the measurement. This error can be reduced by using a precise measuring device. The systematic errors we have include air resistance of the mass and string moving through the atmosphere. b) Observations I observed that time period should not be change when we change amplitude, mass, but it does change in our experiment because we were not performing the experiment in the perfect atmosphere. I also observed that length does change the result a little bit, I’m not sure if it is changing because of gravity or what, but it is changing. I think this should be explained in lab. c) Suggestions I will suggest instead of using cellphones as stopwatches we should use photogates for better results. Also we should perform some extra trails for better results, and then average them. For time period we should use minimum 10 oscillations or more than that. I also suggest never push the ball, just release it from the distance, if you push the results will never be good. 6- Conclusion After completing three experiments, we concluded that the only factor affecting the time of the swing of a pendulum was the length of the string. The time increased as the length of the string increased. Mass, and amplitude does not affect the time, time remains the same for both. But we used wooden ball so the air resistance affects the wood more than metal so we got some different times, because of this. If we have used both same material ball, with different masses, I think there will not be any difference. Also we were not doing the experiment in perfect atmosphere so if our time has differences, this is because of friction and air resistance. Lab book answer, conclusion: Part 1:- Period of the pendulum is not affected by amplitude as we did experiment we saw that there is not much difference in the results. Part 2:- It also does not depend on mass, as we did experiment there was not much more difference, the difference was because we use two balls of different materials, one wooden, one metal. If we have used both same material balls, but with different masses, I think the results would be much accurate. But our results are still precise. Part 3:- It actually depend on length, as length increases, time decreases. And I think length and time are inversely proportional to each other. Part 4:- Our theoretical values are almost the same as experimental values. Minor differences are still there because of nature, friction and air resistance. Uncertainties :- As I discussed above that equipment affect results a lot. We should use photo sensors instead of using cellphones as stopwatches. Also we should use better equipment for amplitude, as it was not quite perfect as we used a ruler. And also the center of mass on bob was not marked we could have used better equipment for taking length too.