Physics 1 Lab: Period of a Pendulum Purpose: To determine the factors that affect the period of a pendulum and to construct a pendulum with a period of one second. Equipment: stand, pendulum clamp, pendulum bob, string, stopwatch, balance, meterstick, protractor Discussion: A simple pendulum consists of a small heavy ball (the bob) suspended by an essentially weightless string from a frictionless support. The bob is free to oscillate (swing back and forth) in any direction. A pendulum completes one cycle or oscillation when it swings forth and then back to its original position. The time it takes to complete one cycle is called its period. If during a 10­second interval a pendulum completes 5 cycles, its period, T, is 2 seconds (10 seconds divided by 5 cycles). For convenience, the quantity cycle is usually not expressed. The period is then two seconds for this pendulum. What affects the period of a pendulum? When several factors are involved, scientists separate the effects of each by changing only one thing at a time while keeping everything else constant. To do this in our lab, we will change only one pendulum variable at a time (amplitude, mass of bob, length of cord) and keep track of which affect the period and which do not. Procedure: Part 1: Amplitude
· Make a data table on a piece of paper with columns labeled trial number, amplitude, bob mass, length, total time and period and enough rows for 10 trials.
· Choose a pendulum bob and measure its mass.
· Set up a pendulum by suspending the bob from the pendulum support as directed by your instructor. Use a pendulum length as long as possible without hitting the table. Measure the length of the pendulum and record.
· Using the protractor, draw back the bob so that the cord makes a 5 o angle with the vertical. Release the pendulum and allow it to swing freely back and forth.
· Time 10 complete cycles with the stopwatch. Be sure to start and stop the watch at the same point in the pendulum cycle. Record the data as trial 1 in the data table.
· Repeat with amplitudes of 10 o and 15 o for trial 2 and 3, using the same bob and cord length. Part 2: Mass
· Select a bob with a different mass, measure its mass, and replace the original bob with it. Be careful to keep the length of the pendulum the same.
· Time 10 cycles with the new bob using an amplitude of 10 o and record the data as trial 4.
· Replace the bob with a third bob of different mass and time 10 more cycles keeping length and amplitude the same. Record as trial 5 Part 3: Length
· Using the same bob as the previous step, shorten the length of the pendulum by about 10 cm and measure the length of the new pendulum.
· Using a 10 o amplitude, time 10 cycles of the pendulum motion and record as trial 6.
· Repeat for 4 more lengths, each about 10 ­ 15 cm shorter than the trial before. Keep the amplitude and bob the same for all trials in this step. Your final trial should have a length of less than 20 cm.
Physics 1 Lab: Period of a Pendulum Data and Observations
· Calculate the period for each trial in the experiment.
· Determine which of the three parameters had the most effect on the period of the pendulum.
· On a piece of graph paper or using a computer program, construct a graph of period vs. length, using the data from trials 5 – 10. Use the origin as one of your data points. Be sure to include all the components of a good graph.
· Draw a best­fit curve to fit your data.
· Using your graph, determine what the length should be for a pendulum with a period of exactly one second.
· Construct a pendulum with this length and time its period. If its period is not exactly one second, adjust the length until a one­second pendulum is obtained. Questions (answer on your own paper) 1. Which measured quantity for the pendulum had the greatest effect on its period, the mass, the amplitude, or the length? 2. Examine the period for trials 2, 4, & 5. Allowing for a ±10% variation due to experimental error, what effect, if any, does mass have on the period of a pendulum? 3. Examine the period for trials 1, 2, & 3. Allowing for a ±10% variation due to experimental error, what effect, if any, does amplitude (size of swing) have on the period of a pendulum? 4. Examine the period for trials 5 ­ 10. Allowing for a ±10% variation due to experimental error, what effect, if any, does length have on the period of a pendulum? 5. According to your graph, what was the length for your one­second pendulum? Circle this point on your graph. 6. What was the actual length of your one­second pendulum? 7. If you set up your pendulum on the moon, where gravity is one­sixth of earth’s gravity, would the period be less than, greater than, or the same as it would be in our lab? 8. If you set up your pendulum in an elevator accelerating upward, would the period be less than, greater than, or the same as it would be in our lab? 9. If you set up your pendulum in a zero gravity environment of deep space, how would the period be affected? Pre­AP only: 1. In the future, we may send astronauts to land on Mars. In an experiment to find the acceleration due to gravity on Mars, a 75.0 cm pendulum is found to have a period of 2.80 s. Find g on Mars. 2. In 1851, Jean­Bernard­Leon Foucault suspended a 67 meter long, 28 kilogram pendulum from the dome of the Pantheon in Paris to show the movement of the earth. To start the pendulum swinging, it was drawn back to a displacement of 5.0 degrees. Find the work done starting the pendulum.