Lab 7 - Pendulum Lab

Lone Star College Physics 1401 Name: ______________________ Date: _________ Lab 7 – Pendulum Lab Objectives To investigate the pendulum system, and to experimentally determine the value of 𝑔 on Earth’s surface. Theoretical Model According to our understanding of the simple pendulum, the period of a pendulum with length 𝐿 and mass 𝑚 is given by where 𝑔 is the gravitational field at the location of the pendulum. Experimental Procedure • Go to the PhET simulation at https://phet.colorado.edu/en/simulation/pendulum-lab . • Click on the “Lab” tab. • Select “Ruler” and “Timer” from the lower left corner. Do not select the “Period Timer”. Mass 1. Place a 100-g mass on a pendulum of length 0.50 m. 2. Press the “Pause” button just to the right of the stop button at the bottom of the screen. 3. Pull the pendulum upward so that the string makes an angle of 10° from vertical. 4. Hit the play button. 5. Use your stopwatch to record the time required for 10 complete oscillations of the pendulum (hint: wait until the pendulum reaches a maximum or minimum angle and start your stopwatch right at that moment!). We use 10 complete oscillations because it minimizes stopwatch timing errors by allowing us to take an average. Record your value in the Time column of the Data Table for Mass in the 100 g row.

2 6. Compute the time for a single cycle (one period) by dividing by 10 and enter it in the Experimental Period 𝑇 𝑒𝑥? column of the Data Table for Mass . 7. Calculate the theoretically predicted period using equation (1) and enter it in the Theoretical Period 𝑇 𝑡 ℎ 𝑒? column of the Data Table for Mass . Use 𝑔 = 9.80 m/s 2 . 8. Calculate the percent error between the theoretical and experimental periods and enter it in the Percent Error column of the Data Table for Mass . Your percent error should be quite low. If it is higher than 1 or 2% then you most likely either did your theoretical calculation incorrectly or made a timing error in your measurement. 9. Repeat steps 1 through 8 for the remaining masses in the Data Table for Mass . (Data Table:10 pts) Data Table for Mass (All lengths = 0.50 m) Mass Time (s) Experimental Period 𝑇 𝑒𝑥? (s) Theoretical Period ( 𝑇 𝑡 ℎ 𝑒? ) (s) Percent Error 100 g 300 g 500 g 700 g 900 g 1100 g 1300 g 1500 g Length 1. Hang a 100-gram mass on a pendulum of length 0.20 meters. 2. Press the “Pause” button just to the right of the stop button at the bottom of the screen. 3. Pull the pendulum upward so that the string makes an angle of 10° from vertical. 4. Hit the play button.

4 Calculations and Analysis NOTE: You will be creating two plots in this lab. You must attach these plots to your lab report! Theoretical Model As stated previously, according to our understanding of the simple pendulum, the period of the pendulum is given by In questions 1-3 below, refer strictly to equation (1) above, not to the data you took in your experiment. In your answers to questions 1-3, there should be no reference to your data from the experiment. 1. Imagine you were to create a plot, with the period 𝑇 on the y-axis and mass 𝑚 of the pendulum on the x-axis. What type of curve would you expect this plot to follow, based on the theoretical model above (equation (1))? Do not use the data you just took to inform your answer. Answer strictly based on the theoretical equation for the period. i. A constant (horizontal) curve? ii. A linear curve? iii. A quadratic (parabolic) curve? iv. A square root curve? v. Another type of curve, such as cubic, exponential, etc…? Circle an answer from above and explain your answer briefly below. (Ans:3pts) 2. Imagine you create a plot, with the period 𝑇 on the y-axis and length 𝐿 of the pendulum on the x- axis. a) What type of curve would you expect this plot to follow, based on the theoretical model above (equation (1))? Do not use the data you just took to inform your answer. Answer strictly based on the theoretical equation for period.

5 i. A constant (horizontal) curve? ii. A linear curve? iii. A quadratic (parabolic) curve? iv. A square root curve? v. Another type of curve, such as cub ic, exponential, etc…? Circle an answer from above and explain your answer briefly below. (Ans:3pts) b) Would you expect a linear best-fit function to be useful in this case? Explain briefly. (Ans:3pts) 3. Imagine you create a plot with the period 𝑇 on the y-axis and the square root of the length √ 𝐿 on the x-axis. a) What type of curve would you expect this plot to follow, based on the theoretical model above (equation (1))? Do not use the data you just took to inform your answer. Answer strictly based on the theoretical equation for period. i. A constant (horizontal) curve? ii. A linear curve? iii. A quadratic (parabolic) curve? iv. A square root curve? v. Another type of curve, such as cubic, exponential, etc…? Circle an answer from above and explain briefly below. (Ans:3pts) b) What term from equation (1) would correspond to your “y - value”? (Ans:3pts) c) What term from equation (1) would correspond to your “x - value”? (Ans:3pts) d) What term from equation (1) would correspond to your “slope”? (Ans:3pts) e) What should your “y - intercept” be? Explain briefly why you would expect this value for the y - intercept. (Ans:3pts)

7 6. Using the data table for Length , create a scatterplot with the experimental period 𝑇 𝑒𝑥? on the y- axis and the square root of the length √ 𝐿 on the x-axis. Include a best-fit line with equation and 𝑅 2 value as usual. Refer to the Data Analysis Guide for procedures required to create a proper plot. (Attached your plot below). ( 𝑇 𝑒𝑥? the y-axis vs. square root of the length on the x-axis graph – 10pts) Write the equation of the best-fit line, as well as your 𝑅 2 value, in the space below: (Ans:3pts) 7. Based on your plot, are the period and the square root of the length strongly correlated? In other words, does the shape of the plot match your expectation from question 3a above? Explain your answer, using your 𝑅 2 value in your explanation. (Ans:3pts)

8 Solving for the Gravitational Field Now assume that you do not know the value of the gravitational field 𝑔 on the surface of the Earth (where your pendulum is located). You will use the data from this lab to determine its value. 8. Using your best-fit function and your answer to question 3d above, solve for the best-fit experimental 𝑔 value ( 𝑔 𝑒𝑥? ) on the surface of the Earth. Show your work below! (Ans:3pts) 𝑔𝑒𝑥? = ______________________________________ 9. Compute the percent error between your experimental value of 𝑔 and the accepted theoretical value of 𝑔 . (Ans:3pts) % error = _____________________________________