2021 Version Newton's Law of Universal Gravitation Name: In this experiment, you will use a simulation to measure the gravitation force between two masses. You'll determine how the strength of the force of gravity depends on the two masses and the distance between them. You'll also determine a value for the Universal Gravitation constant, G, using graphical analysis. Essentially you are validating Newton's Law of Universal Gravitation Law that is modelled mathematically as: F = Gin, mz 12 Where F, is the gravitational force between two masses in Newtons, m is mass of object in kilograms, r is distance between the centre of the objects in meters. To run the simulation, go to phet.colorado.edu/en/simulation/gravity-force-lab and click on Run Now. PART 1. WARMUP - QUALITATIVE OBSERVATIONS (NOT MARKED) 1. Use the slider on the right-hand side of the screen to increase the mass of ml. Does the gravitational force between the two masses increase, decrease, or remain the same? 2. Decrease the mass of ml. Does the gravitational force increase, decrease, or remain the same? 3. Use the second slider to increase the mass of m2. Does the gravitational force increase, decrease, or remain the same? 4. Decrease the mass of m2. Does the gravitational force increase, decrease, or remain the same? 5. Click on either one of the two masses and drag it so they are closer together. Does the gravitational force increase, decrease, or remain the same? 6. Drag either mass so they are farther apart. Does the gravitational force increase, decrease, or remain the same? 7. In any of your observations so far, have the two gravitational forces (on ml from m2 and on m2 from ml ) ever been different from each other? Why?PART 2. QUANTITATIVE MEASUREMENTS PART 2A: F, vs mimz Question: How is gravitational force (F ) related to the magnitude of the mass of two masses mj and mz)? Use the simulation to collect 7-10 data points in order to answer the question above. Observations: Radius (controlled variable): mi (kg) my (kg) F. (N) Analysis Complete a data table below and create a gravitational force as a function of the product of the masses graph. Note: While you can graph by hand, I encourage you to use Excel or Google Sheets to create your graph. mime (kg ) F: (N)\fPART 2B: F, VS r Question: How is gravitational force (F ) related to the separation distance of two masses (my and my)? *The separation distance is defined as the distance between the centers of the two objects; the best strategy involves centering the objects on a gridline and using distances that are a whole number of squares. Observation: Using the simulation to collect 7-10 data points in order to answer the question above. The values used for my and my should stay constant for all trials. Write the values you used down: mi: Separation Distance (m) | Gravitational Force (N) Analysis: Graph the data in order to describe the relationship between gravitational force and the separation distance. Note: While you can graph by hand, I encourage you to use Excel or Google Sheets to create your graph.\fPART 2c: Straighten the curve The graph in 2B) is not a linear graph so its slope cannot be determined. Thus, we need to manipulate the data in order to create a linear graph. Please review the lesson on Manipulating Graphs (in D2L Content > Before you start > Math Skills) for more information. Analysis: Create a linear graph by manipulating the original data in order to produce a straight-line graph. Note: While you can graph by hand, I encourage you to use Excel or Google Sheets to create your graph. Adjust the settings so that you display the equation of the line The mass values used in part 2B remained constant and are again used in part 2C. Write these value down again: mi: 12: Separation Distance (m) Gravitational Force (N)\fPART 3. ANALYZE YOUR DATA Relate the slope of the linearized graph to Newton's Universal Gravitation equation to determine the Universal Gravitation constant for your graph in Part 2c Use the slope of the line of best fit in 2c) to find the experimental value of the Universal Gravitational Constant ("G"). 1) If you made the graph by hand, you'll need to calculate the slope using two points on the line other than the data points. 2) If you used Excel or Sheets, adjust the setting so that it shows the equation of the line. It will be in the "slope - intercept form" (i.e. "y mx+b") 3) Compare the equation for Universal Gravitation with the equation of a line in slope - intercept form. Clearly identify which variables or groups of variables in the former equation is analogous to the variable in the latter equation. (That is, which variable(s) in the Fg equation is "y", "x", and "m: the symbol for slope") 4) Using your answer in 3) and the value of slope of the line of best fit, solve for G State the relationship (direct, square, inverse square) for each of the graphs that you created in this lab. Determine the accuracy of your experimental value of G by finding the percent error: %Error = Theoretical - Experimental -x100 Theoretical Identify one way that this simulated lab can be improved.LAB ASSESSMENT - Process Skills Evaluated Data is complete, well organized and recorded appropriately Graphing Skills appropriate title labeled axes FI appropriate scale accurate plotting of values mama line of best fit is sketched Newton's Law of Universal Gravitation Mathematical calculation of slope is completed for final graph using GRASP or display of formula on computer generated graph Slope is related to Newton's Universal Gravitation Relationship is stated for cach graph Calculation of % difference is made How lab could be improved. Mark /28 Lab adapted from Phantastic Physics Phun with PHET by Kristian Basaraba