Laws of Attraction Part 1
Which variable matters the most? (Universal Law of Gravity)
This activity can be done as a two part activity. Part 1 explores the universal law of gravity equation. Part 2 examines which celestial body in our solar system has the largest pull on the Earth.
Background
Humans spent decades figuring out how to escape the gravitational pull on this planet to get out into space. It took literal rocket science to make it happen. The crazy part is that the Universal Law of Gravity (ULG) says that the force of attraction is not just between humans and the Earth, the Earth and the Sun, or the Moon and the Earth. If the ULG is correct, it means that anything with mass has a pull force between anything else with mass. That gross spider you thought you were repulsed by? You are actually attracted to it. A piece of broccoli on your plate? Attracted. This computer? Even though you may be feeling resentful about having to do some problem solving on it today, you are in fact, attracted. And this computer is attracted to you right back, the exact same amount.
Dataclassroom side note: But why then aren’t we sliding into each other, stuck to everything in our universe? The reason is twofold: 1) because the gravitational force of the earth is faaaaar greater than the gravitational force between you and your computer, and appears to win the pull contest. And 2) because you’re getting pulled onto the Earth, the force between other objects has to also overcome friction forces. And again, these Earth-pull forces are way bigger than attractive force, allowing you to stay in place.
If, however, we were far enough away from the Earth with no friction to speak of, and you had enough time, you and the computer would find yourselves coming towards each other.
Today we’re going to explore a dataset and determine how two of the most important variables of the ULG - mass, and distance between masses - affect the force of attraction. Which matters most?
Dataset
This data set was gathered through a simulator. You can add your own data by going to a site like PHET’s Gravity Force Lab simulator. For each experiment, the variable that was not being manipulated was set to these values:
Mass 1: 100 kg
Mass 2: 6000 kg
Distance between objects (measured from center of mass): 5 m
Variables
Trial # - This categorical variable simply references the trial for which these data were recorded.
Mass 1 (kg) - This numerical variable references the amount of mass contained in the first object. Measured in kilograms.
Mass 2 (kg) - This numerical variable references the amount of mass contained in the second object. Measured in kilograms.
Distance (m) - This numerical variable references the distance between the two objects, as measured from their center of mass. Measured in meters.
Force (N) - This numerical variable describes the gravitational pull force between the two objects. Measured in Newtons.
Experiment # - This categorical variable describes which experiment is being conducted. For experiment 1, distance is the IV and being manipulated. For experiment 2, mass is the IV and being manipulated.
Activity
Part A: Exploring Experiment 1
In experiment 1, mass 1 and mass 2 remain the same value but distance changes.
Use the Make a Graph tool to create a Distance vs. Force graph by showing Distance on X axis, and Force on Y axis. Include a screenshot of your graph here:
2. Create a regression line. Click Appearance, and select “include zero” for x- and y-axis range. Include a screenshot of your graph here:
3) Does this line look like it fits well for your data points? If not, look for a better fit by changing the type of regression line. Note: When r^2 = 1, that means it’s a perfect fit. Which line do you feel most confident about? Include the equation below, as well as screenshot of the new fit.
Extension A: if it is not a linear fit, you need to linearize to confirm you have selected the correct pattern. To do this:
In table view, click the … at the column header.
Go back into the data table and transform the Distance variable while creating a new column.
Select the function you think will create a linear fit.
If you have evidence it’s a good fit (look at your r value), then use that as your answer. Otherwise, try a different transformation of data.
Include a screenshot below as evidence of your linear graph. Include the new equation below the screenshot.
4. Finalize your force vs. distance graph equation by substituting your variables and units in the place of “x” and “y” in your equation.
Part B: Exploring Experiment 2
In experiment 2, mass 2 and distance remain the same value but mass 1 changes.
Change which experiment data we are looking at by excluding experiment 1 and un-exclude experiment 2.
5) Create a graph showing how force and mass are related. Set mass 1 as the x-variable and keep force as y-variable. Remove the regression line for now. Screenshot your graph and include below:
6. Now add back your regression line. Which regression line type seems to fit our length pattern (the non-vertical pattern) best? Note: When r^2 = 1, that means it’s a perfect fit. Extend the line to cross the x- or y- axis.
Which line do you feel most confident about? Include the equation below, as well as screenshot of the new fit:
NOTE: Even though the values are incredibly small, for this dataset they may still be significant, as we are dealing with very small values in general.
Extension B: if it is not a linear fit, you need to linearize to confirm you have selected the correct pattern. To do this:
In table view, click the … at the column header.
Go back into the data table and transform the Distance variable while creating a new column.
Select the function you think will create a linear fit.
If you have evidence it’s a good fit (look at your r value), then move onto the next question below! Otherwise, try a different transformation of data.
Include a screenshot below as evidence of your linear graph. Include the new equation below the screenshot.
7. Finalize your mass vs. force graph equation by substituting your variables and units in the place of “x” and “y” in your equation.
8. To the right is the equation known as the Universal Law of Gravity for the force between two masses. How do the equations you found for mass vs. force and distance vs. force provide further evidence for this equation?