# Pendulum Investigation

Plan Aim To investigate how the length of a simple pendulum will affect the time for a full swing. Variables Length The length of the pendulum has a large effect on the time for a complete swing. As the pendulum gets longer the time increases. As the pendulum gets shorter the time decreases. Air resistance A big and light pendulum bobble would be affected by a major amount of air resistance. This might cause the pendulum to move in a different way. With a little pendulum bobble there is very small air resistance. This can easily be observed because it takes an extended time for the pendulum to stop swinging, so only a small amount of energy is lost on each swing. Gravity The pendulum is motivated by the force of gravity acting on it. The more gravity the shorter time it will take for a complete swing. The less gravity the longer it would take for a complete swing Size of swing The size of the swing does not have large effect on the time. Mass The mass of the pendulum does not affect the time at all.

Prediction The diagram shows the arcs through which two pendulums swing. The red one is twice the length of the black one. The black arc is always at a steeper angle than the red arc, and always above it. The black pendulum has the most gravitational potential energy at the top of the swing because it is higher. This means the kinetic energy and speed through the centre will also be greater. The steeper the arc the greater the acceleration of the pendulum will be. A greater acceleration means a shorter time for each swing. The blue arc has the steepest gradient at the top and is flat when it reaches the middle. The acceleration of the bobble will decrease from a maximum at the top of the swing to zero at the centre. For these reasons, I predict as the string gets longer the time per swing will get longer. Equipment List string, blue-tack, long pin, stopwatch, measuring tape, electronic scale Risks and precautions There are no risks or precautions involved in this experiment Method [image] The string is secured between two small blocks of wood. This ensures that the cotton swings from a single fixed point. A small ball of blue-tack is attached to the bottom end of the cotton and the length is adjusted by pulling the cotton through the two blocks. Gravity may be considered to act through the centre of gravity of the bobble. For this reason the length of the cotton is measured from the wooden blocks to the centre of the bobble. Timings for twenty complete swings are started and stopped as the pendulum passes through the mid-point. A long pin is set up at the mid-point, at right angles to the plane of swing, to provide an accurate reference point. This is achieved by positioning yourself so that you are looking directly along the line of the pin. As the cotton passes the point the stopwatch is started and counting is started at ?0?. The pendulum will swing to one side, and then back through the centre and to the other side. When it passes the centre again ?1? is counted for the first complete swing. In the same manner this process is repeated twenty complete swings. Each process is repeated three times. It is important to ensure that the pendulum is swinging in a single plane before measurements are started. The size of swing must be kept small and accurate. Variable table Dependent Variable value how measured Time for one complete swing (Period) Time for 20 swings. 3 repeats for each length digital stopwatch Independent Variable length 5,10,20- 180cm in 20cm steps ruler Control Variables size of swing small (10Â? or less) protractor mass 10g electronic balance air resistance very small n/a gravity 10 N/kg Trial data 1. Altering the length the length was altered by a measurement of 20 cm. The time increased as the length increased but by a factor of 1.4 approximately. length (cm) mass (g) displacement (cm) time (20 swings) (seconds) 20 10 10 18.10 40 10 10 25.41 2. Altering the mass of the bob The mass was altered by a measurement of 20 grams. This had a small effect on the time. length (cm) mass (g) displacement (cm) time (20 swings) (seconds) 60 5 10 31.02 60 25 10 31.16 3. Altering the displacement of swing the size of the swing was changed by a measurement of 20 cm and this had little effect on the time. length (cm) mass (g) displacement (cm) time (20 swings) (seconds) 60 10 10 31.05 60 10 20 31.39 From the trial data I found the only variable that made a major difference was the length of the pendulum. Results -?? Pendulum length (cm) length (âˆšcm) Number of swings Timings 1st 2nd 3rd Average time average time 1 swing (sec) 5 2.24 20 9.10 8.77 9.36 9.07 0.45 10 3.16 20 12.86 12.79 12.82 12.82 0.64 20 4.47 20 18.15 18.13 18.20 18.16 0.91 40 6.32 20 25.60 25.32 25.87 25.29 1.26 60 7.75 20 31.17 31.21 31.12 31.16 1.58 80 8.94 20 35.90 35.88 35.95 35.91 1.79 100 10.00 20 40.12 40.15 40.07 40.11 2.00 120 10.95 20 43.82 43.90 43.86 43.86 2.19 140 11.83 20 47.92 47.97 47.98 47.95 2.39 160 12.65 20 50.15 50.10 50.10 50.11 2.50 180 13.41 20 53.39 50.44 50.45 52.42 2.62 Control variables mass of bobble = 10g size of each swing kept small and accurate (max displacement approximately 10cm. Analysis and Conclusions Graph1 shows that the time for each swing increases as the length increases and the gradient of the graph decreases as the length increases. Graph2 shows each swing plotted against the square-root of the length. This gives a straight line graph through the origin. Using the equation: Y=mx (used for straight line graphs through the origin) the gradient Â?XÂ? measured The gradient ?m? measured = 2.5Ã?13.5 = 0.19 If Â?TÂ? is the time for one swing in seconds, and Â?LÂ? is the length in centimeters, the equation for the line is written as: T = 0.19âˆšL Conclusions The time for one complete swing is proportional to the square root of the length. All the points for Graph2 lie on a straight line so the conclusion is very reliable over this range. It seems likely that the same trend would continue if the length was extended. Shorter lengths look like they would also follow the same pattern despite the fact that it gets more difficult to take the measurements as the time gets shorter. For very short lengths the trend might not continue and would be extremely difficult to measure. Evaluation Measuring the length A difficult part of measuring the length is make your mind up where the centre of the bobble is. The uncertainty in determining this measurement is probably about 1-2 mm. . The total error in measuring the longest and shortest length is not likely to be more than a millimeter. Adjusting the length of the pendulum was time consuming but was not a problem in the path of accuracy. The string could be accurately pulled through the wooden blocks to the required lengths. Measuring the time The stopwatch I used, measures to one hundredth of a second even though the overall accuracy of the time measurements are so accurate. The human reaction time to start and stop the watch roughly cancel each other out as the same event is being observed, and reacted to in the same way, each time. Errors are produced by any variability in the reaction time of the individual which could be affected by various things. The even trend in the graph specifies that the results are accurate and dependable. There are no irregular results to be seen in the trend of the graph. Reliability No significant problems or difficulties were met when performing this investigation. The accuracy and reliability of the results and conclusions are incredibly good. From the accuracy method applied and for the range of values tested, it is quite understandable that the time for a simple pendulum takes for a complete swing is proportional to the square-root of the length. Improvements The procedure used was simple and straightforward and no difficulties were encountered. A small improvement could be made regarding the measuring of the length pendulum. A piece of wood, could be placed level with the point of suspension, and a set square could be placed along the flat side and just touching the bottom of the pendulum. This distance could then be measured extra accurately than trying to guess where the middle of the bobble is. More attempts could be taken but I do not think it is necessary or would make a significant difference to the morals of the conclusion. Longer lengths could be tried, up to whatever lengths desired. If the pendulum gets very long a stronger string will be needed and a bobble in ratio. Extending the investigation Extending the investigation would mean extend the range of lengths tested and observing if the same trend continues.

Pendulum Investigation
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