PHYS 201 Lab Report 3

PHYS 201L Section 004 Simple Pendulum Oluwaseyi Adelakun & Anna Sandwell I. Table of Data. Metal Ball l (m) t 1 (s) t 2 (s) t 3 (s) <t> avg g (m/s 2 ) % d 0.2 0.917 0.824 0.834 0.858 10.7 9.44 0.4 1.27 1.27 1.27 1.27 9.79 0.0918 0.6 1.53 1.53 1.53 1.53 10.12 3.27 0.8 1.81 1.81 1.81 1.81 9.64 1.63 Wooden Ball l (m) t 1 (s) t 2 (s) t 3 (s) <t> avg g (m/s 2 ) % d 0.2 0.917 0.916 0.919 0.917 9.39 4.18 0.4 1.24 1.23 1.23 1.23 10.44 6.53 0.6 1.52 1.52 1.52 1.52 10.25 4.59 0.8 1.79 1.80 1.78 1.79 9.86 0.582

II. Calculations. Metal Ball g = 4π 2 l / <t> 2 g [0.2] = 4π 2 (0.2) / (0.858) 2 = 10.7 g [0.4] = 4π 2 (0.4) / (1.27) 2 = 9.79 g [0.6] = 4π 2 (0.6) / (1.53) 2 = 10.1 g [0.8] = 4π 2 (0.8) / (1.81) 2 = 9.64 % d = | g exp - 9.8 / 9.8 | x 100 % d [0.2] = | (10.7) - (9.8) / (9.8) | x 100 = 9.4 % % d [0.4] = | (9.79) - (9.8) / (9.8) | x 100 = 0.0918 % % d [0.6] = | (10.1) - (9.8) / (9.8) | x 100 = 3.27 % % d [0.8] = | (9.64) - (9.8) / (9.8) | x 100 = 1.63 % Wooden Ball g = 4π 2 l / <t> 2 g [0.2] = 4π 2 (0.2) / (0.917) 2 = 9.39 g [0.4] = 4π 2 (0.4) / (1.23) 2 = 10.4 g [0.6] = 4π 2 (0.6) / (1.52) 2 = 10.3

Free Body Diagram Our Free Body Diagram showcases all the forces acting on the pendulum bob while it is at its maximum in swing. The forces acting on the pendulum are tension and gravity, but we also must take the components of the pendulum vector into account. IV. Questions & Calculations. 1. What is the expected relationship between the length of a simple pendulum and its period? Does your data follow the expected trend? The expected relationship between the length of a simple pendulum and its period is that as the length increases, the period it takes for the ball to complete a full cycle should also increase. In our experiment, we found that our data does follow the expected trend. As we increase the length of our pendulum between 0.2 and 0.8 meters, we also see a steady increase in the time required for a full swing. 2. From graph 1, determine g, the acceleration of gravity. Is this a good way to determine g? What limits your precision? Does your value of g agree with the expected value?

The acceleration of gravity from our graph is 9.413 for the metal ball and 9.974 for the wooden ball. Because we know the expected value of g is 9.8, one can say that this is a good way to determine g. It would be best to calculate the percent error of our data to represent the accuracy of our results. Potential errors could have arrived through our measurement of the length of the pendulum, the time period in which the pendulum oscillated, and our assembly of the experimental apparatus. 3. Did the mass of the bob have an effect? The mass of the bob did not have an effect in the pendulum. Our experimental results remained consistent for both the metal and wooden ball. The only factor that influences the pendulum is the acceleration due to gravity, which remained constant for both masses. 4. Instead of using the timer to measure the period of many individual oscillations, how would you find the period with good accuracy using a stopwatch? You could find the period of individual oscillations by recording a number of oscillations for a particular amount of time, and divide that number by the total time recorded by the stopwatch. This value would then give the time period for one individual oscillation. V. Results & Conclusions. Results: The results show that the mass of the ball did not affect the time of the pendulum. Both balls had almost identical slopes and the R^2 is close to one for both graphs. We changed the length by raising it 20 cm (or 0.2m) incrementally and watched as the time gradually increased. This displayed a direct relationship between length and time. After calculating the standard deviation, 6/8 of the data points had a percent lower than 5 meaning that the data was accurate.