Explore how the variables of a pendulum affect its swing with this classic physics dataset. Use your understanding of pendulum swings to solve the problem in this scenario.

Background

Pendulums have been useful as a way for us to keep time since Christiaan Huygens invented the first pendulum clock in the early 1600’s. By understanding how they function, people have been able to harness these accurate timekeepers for many applications throughout history such as grandfather clocks and metronomes.

Pendulums can show up in other places too. You have been hired as a stunt coordinator for a movie, to help the crew with the physics of an action movie.  A scene is coming up where a leading movie star will be escaping a pack of wild animals by swinging on a vine across the river.  The director calls upon you to be able to inform him just how long it will take her to get across the river.

Your job today is to use a model to determine how mass, length, and angle affect the swing of a pendulum. Once you find the relationship, you will be able to submit your recommendation to the director.

*This is clearly a fictional scenario for a physics story problem. In real life a strong understanding of physics is absolutely necessary to even think about a career as stunt coordinator!!!!

Dataset

Data were collected using an online simulator by PhET.  Twenty-six trials were run in total.  During these trials, one of each of the three variables (Angle, mass, length) was investigated individually.  In trial 1-10, mass was manipulated with angle and length held constant. Trials 11-16 manipulated angle with mass and length held constant. Trials 17-26 manipulated length with mass and angle held constant.  

Summary table for the experimental design:

When held constant, the variable values were:

Length:  0.5 m
Mass:    0.5 kg
Angle: 15.0 degrees

Acceleration due to gravity is: 9.8 m/s/s

Variables

The variables should be explained and defined very clearly so that logical conclusions and interpretations can follow from analysis.

Trial # - This numeric variable simply references the assigned number for each trial when data were collected. This is not a measurement and there is no associated unit.

Manipulated Variable - This categorical variable describes which variable was investigated during an individual trial.  The variables that were not listed were held at the “constant” value.  

Angle - This numeric variable is the angle displaced from “rest”. Measured in degrees.

Mass - This numeric variable is the amount of mass added to a pendulum.  Measured in kilograms.

Length - This numeric variable is the measurement from center of mass on pendulum to pivot point. Measured in meters.

Period - This numeric variable is the amount of time for the pendulum to complete one oscillation. Measured in seconds.

Activity

1. Use the Make a Graph tool to create a Trial # vs. Period graph by showing Trial # on X axis, and Period on Y axis.  Differentiate between the data by showing Manipulated Variable on the Z (color coding) axis.Paste a screenshot of your graph here:

2. Which data points seem to show similar patterns?

3. Which variable matters when it comes to changing period?

4. Describe what you’re seeing in the data as evidence for your answer to #3.

5. Now, investigate just Length vs. Period by showing Length and setting it as your x-axis. You can keep Manipulated Variable on for the z-axis. Include a screenshot of your graph here:

6. How would you describe length’s effect on the period of a pendulum? 

7. We need to create a regression line to find the exact relationship.  Turn on regression lines, and choose the type of regression line from the dropdown that seems to be the best fit.  Which is it? Use your regression line to write a final equation for what affects the period of a pendulum. (Hint - do not write x and y, but use the actual variables in their place). Paste a screenshot of your graph as evidence of a match.

8.  Using your equation, predict how long it would take our movie star to escape the rampaging animals!

Mass of actress:        59 kg
Length of vine:          10 m
Angle of release:       15 degrees

(Hint: think about the definition of a period versus the actress’s motion to get across a river before calculating)

9. If her stunt double has to replace her (65 kg), how will they need to change the timing of the shot?

Linearization Extension -- The most definitive proof of a relationship is a linear fit. Go back into the data table and create a new column by transforming the Length data. Select the transformation function you think will create a linear fit when plotted on X with Period on Y Paste a screenshot below as evidence of your linear graph. Include the equation of the function below the screenshot.  

Use your regression line to write a final equation for what affects the period of a pendulum. (Hint - do not write x and y, but use the actual variables in their place).

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