UNIVERSITY OF GAZIANTEP DEPARMENT OF ENGINEERING OF PHYSICS EP 135 GENERAL PHYSICS LABORATORY I REPORT FOR EXPERIMENT 1 MEASUREMENT OF GRAVITATIONAL ACCELERATION WITH SIMPLE PENDULUM (do not write this: Repeating Experiments) Group I Isaac Newton Albert Einstein Werner Heisenberg Abdus Salam Date of Experiment : Date of Submission : Deadline : 18.11.2011 22.11.2011 25.11.2011 Lab Assistant(s): Res. Ass. Hüseyin Toktamış Res. Ass. L. Hasan Çite Page 1/5 1. OBJECTIVE The purpose of the experiment is to determine the gravitational acceleration, g, by measuring the period of a simple pendulum. 2. THEORY The simple pendulum is an example mechanical system that exhibits periodic motion. It consists of a particle-like bob of mass m suspended by a light inextensible string of length L that is fixed at the upper end, as shown in Figure 1. The motion occurs in the vertical plane and is driven by the gravitational force. Figure 1. A simple pendulum The acceleration due to gravity for small angle swings of a simple pendulum (small dense bob on a light inextensible string) is given by[1]: = 4π2 2 (1) where T is the period of the oscillation for the pendulum. 3. EXPERIMENTAL SETUP AND EQUIPMENTS Apparatus: String, stop watch, meter stick, bob, support rods. The pendulum consisting of the string and bob is attached to meter stick via support rods as shown in Figure 2. The bob is manually pulled such that the pendulum makes a small angle (such as 5o) with respect to vertical direction. The time for the required number of oscillations of the pendulum is recorded by a stop watch. The period is calculated by dividing the total measured time to number of oscillations counted. Figure 2: The experimental setup Page 2/5 4. PROCEDURE i. Make a simple pendulum by using the support rods, bob, and string as shown in Figure 2. ii. Construct a data table to record the following data for each trial. Length (L), Initial angle (θ), Number of oscillations (N), Total time taken for the number of oscillations (t), Measured period (T=t/N). iii. Use stop watch to measure the time it takes the pendulum to complete 10 oscillations iv. For the initial angle 5o, repeat the experiment for the fixed length L = 1.0 m, 15 times. Record measured time values for each trial v. Calculate g for each trial, evaluate the mean value, standard deviation and standard error of Record the result, in the form of g ± σE. vii. Compute percentage error to compare your result (g in previous case) with the very well known measured value of 9.80665 m/s2[2]. 5. RAW DATA Page 3/5 6. DATA ANAYISIS Table 1 shows calculated g values using Eqn (1). Since number of data is enough to find mean and standard deviation, it is not necessary to compute the error propagation for each measurement. Table 1: Measured periods and corresponding calculated values of g. Measurement Time for 10 Period Calculated g (m/s2) # oscillations t(s) T = t/10 (s) Eqn(1). 1 20.05 2.005 9.8204 2 20.09 2.009 9.7814 3 20.04 2.004 9.8302 4 20.04 2.004 9.8302 5 20.12 2.012 9.7522 6 20.09 2.009 9.7814 7 20.09 2.009 9.7814 8 20.09 2.009 9.7814 9 20.08 2.008 9.7911 10 20.04 2.004 9.8302 11 20.06 2.006 9.8107 12 20.09 2.009 9.7814 13 20.06 2.006 9.8107 14 20.06 2.006 9.8107 15 20.04 2.004 9.8302 Using Excel program or pocket calculator, we can compute the mean value, standard deviation and standard error of the data above as follows: = ∑ 9.8204 + 9.7814 + ⋯ + 9.8302 = = 9.8016 m/s2 15 ∑( − )2 (9.8204 − 9.8016)2 + ⋯ + (9.8302 − 9.8016)2 =√ =√ = 0.0245 m/s2 −1 15 − 1 = σ √ = 0.0245 √15 = 0.0064 m/s2 7. RESULTS The measured gravitational acceleration is: 9.8016 ± 0.0064 m/s2 The percentage error between the world best value and this measurement is = |9.8016 − 9.80665| × 100% = 0.05 % 9.80665 Page 4/5 8. CONCLUSION By means of the simple pendulum, the gravitational acceleration was measured as 9.8016(64) m/s2. To do that, the period of the pendulum was computed from 10 oscillations of the pendulum. To get standard error, the measurement was repeated for 15 times for the fixed length of 1.0 m. The measured g was reasonably close to the world’s best accepted value listed in [2]. The percentage error between our measurements and the accepted value was found to be 0.05%. 9. REFERENCES [1]. “Physics for Engineers and Scientist”, Serway, 6th Ed. Chapter 15. [2]. http://physics.nist.gov/cuu/Constants/index.html - Fundamental Physical Constants. Page 5/5

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