## Tuesday, January 29, 2019

### Determining gravity with a pendulum Essay

Gravity is a pierce that acts on Earth every day. Sir Isaac delinquent no.th was first to under descent the principles of sombreness when an apple fell on his head (Ashbacher 2002). He stated that each particle with a mass attracts totally other particles with mass with a gravitative force that is straight proportional to the product of their masses and reciprocally proportional to their distance of separation squ ared (Ashbacher 2002). This is collectable to that gravity acts amidst inclinations (Ashbacher 2002), consequently ca development a force of attraction which pulls the two aspiration together, such as that an object with a mass will revert down towards earth ground.The Earths mass creates a gravitative force, which pulls the object down towards Earth. This theory is also supported by Newtons three law of questions, particularly the first law stating that, an object in motion or at rest will bear on in motion or at rest unless acted upon by an immaterial fo re. An object will remain at rest drifting in the air, however since an external force, gravity, acts upon it, the object falls towards Earth. Theoretically, the speedup due to gravity on Earth is 9. 8ms-2, however it can also be determined through the use of the equation T = 2? WhereT = succession it took for the p overthrowulum to wheel (s) L = distance between pin tumbler particular and center of the pendulum (m) g = look upon of acceleration due to gravity (ms-2) In order to determine the acceleration due to gravity, the equation were to be staged to g = Equipment  Scissors Pendulum (approx 300g)  Whiteboard draw HangerWhiteboard Texture  Whiteboard Texture Holder   ungainly Tape 2m String * full point Watch Method 1. Set up the pivot foreland location on the whiteboard as shown in the diagram 1. 1 in appendix 1 by using the aroused immortalize to tape the whiteboard diagram hanger onto the magnetic whiteboard marker holder.1. Sticky tape the mark er holder 1. 5m high, part do sure that the magnetic metric grain holder is immovable and secured. 1. Using the measuring tape measure go forth 90cm on the 2m string then using the scissors cut the string, while making sure that the string is cut above 90cm as nigh measurements are required for the purpose of tying. 1. Tie one end of the strengthened string onto the center of the pendulum and the other end of the string onto the pivot menses (end of the whiteboard diagram hanger), while making sure that the real(a) aloofness from the pivot point to the center of the pendulum is 90cm.1. Using the whiteboard marker and ruler, rule a cable television directly from the pivot point to the center of the pendulum (NOTE the length of the line should be 90cm) on the whiteboard. 1. Rule a 7. 9cm line horizontal to the left wing from the point where the center of the pendulum is located. 1. Using the ruler and whiteboard marker, join the pivot point to the end of the 5cm horizontal line. 1. Slowing lift the pendulum to the recent ruled line, while making sure that the string connecting to the pendulum and pivot point remains straight. 1.Release the pendulum slowly. 1. stand the pendulum to throw for two rounds then using the stopwatch start the timer. 1. Stop the timer when the pendulum reaches ten musical rhythms, excluding the first two calendar methods. This gives the it time it took to rhythm method of birth control 10 times. 1. Repeat steps 8-11 three more times. 1. Repeat steps 3-12 provided using a 60cm string with a 5. 2cm horizontal line to the left from the point where the center of the pendulum is located and 30cm string with a 2. 6cm horizontal line to the left from the point where the center of the pendulum is located.Results The Time it Took for a Pendulum to Swing and roll Ten Times Trials Length of Pendulum (m) 1 2 3 clean 0. 30 10. 9 11. 3 10. 2 10. 8 0. 60 15. 8 15. 7 15. 7 15. 7 0. 90 19. 1 19. 0 18. 9 19. 0 Resolution Ruler 0. 1cm Stop Watch 0. 01s Calculations cipher the gravenessal acceleration T = 2? T = 2? g = Calculating Gravitational acceleration for 0. 30m 10. 8s per 10 pendulum vacillation cycle = 1. 08s per pendulum swing cycle L = 0. 30m and T = 1. 08s g = g = 10. 2ms-2 Calculating Gravitational Acceleration for 0. 60m 15.7s per 10 pendulum swing cycle = 1. 57s per pendulum swing cycle L = 0. 60m and T = 1. 08s g = g = 9. 6ms-2 Calculating Gravitational Acceleration for 0. 90m 19. 0s per 10 pendulum swing cycle = 1. 90s per pendulum swing cycle L = 0. 90m and T = 1. 90s g = g = 9. 8ms-2 Calculating Uncertainties for the gravitational acceleration 0. 30m Pendulum Since T = 10. 8 and L = 0. 30, the distrust for T = 10. 8s 0. 05s and L = 0. 30m 0. 05m Highest value for the gravitation acceleration using 0. 30m pendulum is L = 0. 30m + 0. 05m = 0. 35mT = 10. 8s 0. 05 =10. 75s per 10 cycles g = where L = 0. 35 and T = 1. 075s per cycle g = g = 11. 9ms-2 Lowest value for the gravitation accelera tion using 0. 30m pendulum is L = 0. 30m 0. 05m = 0. 25m T = 10. 8s + 0. 05 =10. 85s per 10 cycles g = where L = 0. 25 and T = 1. 085s per cycle g = g = 8. 4ms-2 0. 60m Pendulum Since T = 15. 7 and L = 0. 60, the perplexity for T = 15. 7s 0. 05s and L = 0. 6m 0. 05m Highest value for the gravitation acceleration using 0. 60m pendulum is L = 0. 60m + 0. 05m = 0. 65m T = 15. 7s 0. 05 =15.65s per 10 cycles g = where L = 0. 65 and T = 1. 565s per cycle g = g = 10. 5ms-2 Lowest value for the gravitation acceleration using 0. 60m pendulum is L = 0. 60m 0. 05m = 0. 55m T = 15. 7s + 0. 05 =15. 75s per 10 cycles g = where L = 0. 25 and T = 1. 575s per cycle g = g = 8. 8ms-2 0. 90m Pendulum Since T = 19. 0 and L = 0. 9, the uncertainness for T = 19. 0s 0. 05s and L = 0. 90m 0. 05m Highest value for the gravitation acceleration using 0. 90m pendulum is L = 0. 90m + 0. 05m = 0. 95m T = 19. 0s 0. 05 =18. 95s per 10 cycles g = where L = 0.95 and T = 1. 895s per cycle g = g = 10. 4ms-2 L owest value for the gravitation acceleration using 0. 90m pendulum is L = 0. 90m 0. 05m = 0. 85m T = 19. 0s + 0. 05 =19. 05s per 10 cycles g = where L = 0. 85 and T = 1. 905s per cycle g = g = 8. 2ms-2 Discussion Theoretically the acceleration due to gravitation on earth is 9. 8ms-2. From results, it is shown that when a 0. 30m and 0. 60m pendulum was used, its gravitational pull is compute to be 10. 2ms-2 and 9. 6ms-2. Consequently there is a percentage wrongdoing of 4% and 2% respectively.Since the percentage error is less than 10%, the values are considered acceptable, however when the 0. 90m pendulum was used, its gravitational pull was 9. 8ms-2, which is the like value as the value of the theoretical acceleration due to gravitation on Earth. Within the experiment, the amplitude of the shift key is kept under 7 at 5for all pendulum measurements. Due to this the motion of the pendulum is closely related to the simple harmonic motion (Houston 2012), wherefore the restoring force of when the object swings back to the captain position is directly proportional to the displacement of 5.Due to this the pendulum will continue to swing back to the original base position (Houston 2012), however factors that affects it are the length of the pendulum and the acceleration due to gravity. This controlled factor increases the reliability and accuracy of the results as if the displacement is above 7 then when the pendulum swings, there would be no restoring force, hence there would be less of a chance for the pendulum to return to the original position, and this will affect the cycle time.Nevertheless, uncertainties were calculated for all measurements of the pendulum. For the 0. 30m pendulum, it was calculated from the results that the worst uncertainty for the acceleration due to gravitation is 8. 4ms-2 and highest is 11. 9ms-2. The acceleration due to gravitation from using the time from the three trials is at bottom the range of 8. 4ms-2 and 11. 9ms-2. This is also the same for the 0. 6m pendulum where its highest acceleration is 10. 5ms-2 and lowest is 8. 8ms-2, and 0. 9m where its highest acceleration is 10.4ms-2 and lowest is 8. 2ms-2. Though there were slightly errors presented as the acceleration from the 0. 30m pendulum and 0. 60m pendulum did not correspond with Earths actual gravitational acceleration. One of the errors is believed to be parallax error, which is caused by the difficulty to determine on the nose when the pendulum returned to the original launch position after a full oscillation. This error could have either increased or reduced the time record for the pendulum to oscillate.Thus, by increasing or decreasing the time, it affected the calculation for the acceleration due to gravity for each individual and average measurement. To improve the experiment, a drawn-out pendulum is to be used. This lessens the chance of parallax error hence the oscillation time recorded and lessens the chance of random error, which a lso increases the precision of the data. A long-dated pendulum would cause the time it takes for a pendulum to cycle to be longer as time is proportional to the square root of length.A longer cycle makes it less difficult to record exactly when the pendulum return to its original launch position Conclusion The acceleration due to gravitation was determined to be 10. 2ms-2, 9. 6ms-2 and 9. 8ms-2 for the pendulum measurements of 0. 30m, 0. 60m and 0. 90m. This shows that the aim f the experiment was achieved through the conduction of the experiment. Though, the theoretical acceleration due to gravitation on Earth is determined to be 9. 8ms-2, in which it was found that by using the 0. 90m, the exact value could be calculated. save there were some errors involved such as the parallax error, but within all trials, the acceleration due to gravity of each individual was within the highest and lowest uncertainty range. An improvement was suggested in regards to the errors and that was to use a longer pendulum to reduce the pendulum cycle time. Overall the experiment was followed according to the method, and the result obtained had a percentage error less than 10%, hence the results are considered acceptable.References Ashbacher, C 2002, Sir Isaac Newton The Gravity of Genius, Mathematics & Computer Education, vol.36, no. 3, pp. 302-310, viewed 5 September, via Education Research Complete Houston, K 2012, The Simple Pendulum, College Physics, vol. 1, no. 1, pp. 1-4, viewed 5 September, <http//cnx. org/content/m42243/latest/? collection=col11406/latest> Appendix Diagram 1. 1 Experiment Set Up Show preview just The above preview is unformatted text This student written piece of plump is one of many that can be found in our GCSE Forces and effect section. Download this essay Print Save Not the one?