PHYSICS AND MATH LAB ON GRAVITY NAME

Transcription

1 RIVERDALE HIGH SCHOOL PHYSICS AND MATH LAB ON GRAVITY NAME Purpose: To investigate two of the levels of gravity experienced by Florida teachers during their recent ZeroG flight. Background: NASA supplied the State of Florida a grant to allow teachers to experience weightlessness, and for them to share that experience with their students. Riverdale High School science teacher Dr. Frank Palaia was one of the teachers selected for this experience with 37 other Florida teachers. Two of those teachers (Jeanne Zurewich from Neptune Elementary and Robert Miller of Port Orange Elementary) were able to video portions of the flight which they shared with the other teachers, and portions of these two videos form the basis for this laboratory experiment. Procedure for the Pendulum (Robert Miller video weightless1 ): 1. Watching the pendulum on the video, there are two opportunities to measure the period of the pendulum: during moon-level gravity and during the high-gravity ascending portion of the flight. The effective length of the pendulum (L) is 40cm. 2. For each of the two conditions, use a stopwatch to measure the time it takes the pendulum to make a number of oscillations. Repeat these measurements twice for each of two descents, and record these values on the data sheet. 3. Calculate the period in each case, and obtain the average for each of the two conditions. 4. Using the values for the period, calculate the acceleration of gravity for each case using the formula below and record the values and error calculations on the data sheet.

2 Procedure for the Weight Readings (Jeanne Zurewich video weightless2 ): 1. Watching the scale on the video, there are two opportunities to measure the change in gravitational acceleration: moon ascend moon ascend). You will record on the data sheet the indicated mass of the box of crayons for each second of those four gravitational changes. 2. The scale value of the box or crayons on Earth is 185 grams. 3. The video will be paused each second in order for you to record the scale values. 4. Using these data, you will calculate the acceleration of gravity for each case. 5. Using your knowledge of sinusoids, you will develop a sinusoidal regression to fit the data. Pre-Lab Questions: 1.) State the Law of Universal Gravitation: 2.) State Newton s First Law of Motion: 3.) State Newton s Second Law of Motion: 4.) State Newton s Third Law of Motion: 5.) Define Angular Momentum: 6.) Define Gravitational Force:

3 DATA SHEET FOR GRAVITY CALCULATIONS A. Calculations for the Pendulum 1. FOR THE MOON GRAVITY: TRIAL ONE TRIAL TWO NUMBER OF SWINGS TOTAL TIME (SEC) PERIOD (SEC) AVERAGE X X Using the equation for the acceleration of gravity on the front page, calculate: Moon gravity value = m/s 2 The actual acceleration of gravity on the moon is 1/6 th the value of the acceleration of gravity on Earth. Using this as the accepted value, calculate the percent error of the pendulum experiment for the moon data: Percent Error = Percent Error = ± %

4 2. FOR THE ASCENDING GRAVITY: TRIAL ONE TRIAL TWO NUMBER OF SWINGS TOTAL TIME (SEC) PERIOD (SEC) AVERAGE X X Using the equation for the acceleration of gravity on the front page, calculate: Ascending gravity value = m/s 2 The actual acceleration of gravity during the ascent is approximated as 1.8g, or 17.6 m/s 2 by ZeroG. Using this as an additional value, calculate the percent difference between the values: Percent Difference = Percent Difference = ± %

5 B. Calculations for the Scale Reading: On the second video, there are four readings of the mass of a box of crayons that to be taken: two ascending gravity and two moon gravity. With your partner, read the scale value for each second as the teachers experience the smooth transition from one gravity to the next. Although difficult to read, the left side of the scale has gradations of 10 grams, with indicators at 0, 50, 100, 150, 200, 250, etc. grams. The initial (Earth) mass of the box of crayons is 185 grams. MOON GRAVITY TRIALS x-value TIME SCALE VALUE x -Value TIME SCALE VALUE for time for time 0 1: :52 1 1: :53 2 1: :54 3 1: :55 4 1: :56 5 1: :57 6 1: :58 7 1: :59 ASCENDING GRAVITY TRIALS x -Value TIME SCALE VALUE x -Value TIME SCALE VALUE for time for time 8 1: :25 9 1: : : : : : : : : : : : : : : : : : : : : : : : : : :40

6 For the moon gravity trials: Using the two final values, average them and use this value to estimate the acceleration of gravity value for the moon gravity using a simple proportion. Moon gravity value = m/s 2 The actual acceleration of gravity on the moon is 1/6 th the value of the acceleration of gravity on Earth. Using this as the accepted value, calculate the percent error of the pendulum experiment for the moon data: Percent Error = Percent Error = ± % For the ascending trials: Using the two final values, average them and use this value to estimate the acceleration of gravity value for the moon gravity using a simple proportion. Ascending gravity value = m/s 2 The actual acceleration of gravity during the ascent is approximated as 1.8g, or 17.6 m/s 2 by ZeroG. Using this as an additional value, calculate the percent difference between the values: Percent Difference = Percent Difference = ± % Using the timed data from the scale tables above, plot all of the points in a continuous sequence by omitting the seconds in between the data sets. This will yield an approximate sine curve extending for about 53 seconds.

7 C. Graphing and Analyzing: 1.) Assign each time value an x-value with t=0 being the initial reading. Why would we skip the plateau time periods? 2.) Identify the dependant and the independent variables: Dependant (x): Independent (y): 3.) Using your graphics display calculator plot the independent variable in L1 and the dependant variable in L2. 4.) Next, look at the data and approximate your window x min: y min: x max: x scale: y max: y scale: 5.) Turn your plots on (2 nd, y=) and graph. 6.) At this time make any necessary changes to your window so you can view all data points clearly. 7.) What regression equation would fit this data best? Circle one: Linear Quartic Power Quadratic Natural Logarithmic Logistic Cubic Exponential Sinusoidal Why did you make this choice? 8.) Using the trace feature, or the data itself, identify the period of the function. Period: What does this represent? Solve for b: (hint: ) b =

8 9.) Using the trace feature, or the data itself, identify the amplitude of the function. (hint: ) a = What does this represent? 10.) What is the vertical shift? h = Why is this not 185g (mass of crayons on Earth)? What does this represent? 11.) What is the horizontal shift? k = What does this represent? 12.) Write a sinusoidal regression ( ) for this function. y = 13.) Now use your graphics display calculator to calculate a sinusoidal regression. (stats, calc, sinreg (L1,L2)) y =

9 14.) Calculate your percent error ( ) for: a: % b: % h: % k: % What would account for this error? 15.) Paste this function into Y1 (y=, vars, stats, EQ, RegEQ), and change the line style to bold (move the cursor left to the line and hit enter until it is a bold line). 16.) Type your sinusoidal regression into Y2. Keep this a thin line. 17.) Graph both functions on top of the data points. 18.) Which graph is more accurate? Why do you feel it is more accurate? 19.) Why was this data displayed as a sinusoidal regression rather than any other kind of regression equation?

10 POST LAB QUIZ FOR STUDENTS Quiz on Sections A and B (Science Class): 7.) What is the difference between mass and weight? 8.) What does the gravitational force between two objects depend on? and. 9.) What is the difference between percent error and percent difference? 10.) What is the gravity on the Moon (don t forget to include units)? 11.) True or False: Real life situations fit our scientific rules and laws perfectly. 12.) State the Law of Universal Gravitation: 13.) Newton s First Law of Motion is: 14.) Newton s Second Law of Motion is: 15.) Newton s Third Law of Motion is: 16.) Define Angular Momentum:

11 Quiz on Section C (Math Class): 1.) a.) The independent variable is graphed as the - value. a. The dependent variable is graphed as the - value. b. Identify the independent variable: Height or Age (circle one). c. Identify the dependant variable: Time or Distance (circle one). 2.) What is the standard sinusoidal regression equation? y= From the graph of a sinusoid identify the following: Window: [ 2,2 ] x [ 5,3] 3.) Amplitude: 4.) Period: 5.) Vertical Shift: 6.) Horizontal Shift: Describe a real world situation that would match the distance vs. time graph: The Situation is: This is what is happening: 7.) From 0s to 3.5 s: 8.) From 3.5s to 11 s: 9.) From 11s to 16 s: 10.) From 16s to 18 s: 11.) From 18s to 20 s: 12.) From 20s to 25 s: 13.) From 25s to 29 s:

12 POST LAB QUIZ FOR STUDENTS - KEY Quiz on Sections A and B (Science Class): 1.) What is the difference between mass and weight? 2.) What gravitational force between two objects depends on? Mass and Distance between Them. 3.) What is the difference between percent error and percent difference? 4.) What is the gravity on the Moon (don t forget to include units)? 5.) True or False: Real life situations fit our scientific rules and laws perfectly. F 6.) State the Law of Universal Gravitation: Gravitational forces act on all objects irrespective of their size and position. 7.) Newton s First Law of Motion is: Every object continues in is state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. 8.) Newton s Second Law of Motion is: The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. 9.) Newton s Third Law of Motion is: Whenever an object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. 10.) Define Angular Momentum: The angular momentum of a rotating object remains constant if the net torque acting on it is zero. Quiz on Section C (Math Class):

13 1.) a.) The independent variable is graphed as the x - value. b.) The dependent variable is graphed as the y - value. c.) Identify the independent variable: Height or Age (circle one). d.) Identify the dependant variable: Time or Distance (circle one). 2.) What is the standard sinusoidal regression equation? y= From the graph of a sinusoid identify the following: Window: [ 2,2 ] x [ 5,3] 3.) Amplitude: 3 4.) Period: 4 5.) Vertical Shift: -1 6.) Horizontal Shift: Left 1 Describe a real world situation that would match the distance vs. time graph: The Situation is: Answers may vary This is what is happening: 7.) From 0s to 3.5 s: Going nowhere or traveling at v= 0 m/s for 3.5 seconds 8.) From 3.5s to 11 s: Traveling away 8m in 7.5 s or traveling at v= 1.06 m/s for 7.5 seconds 9.) From 11s to 16 s: Going nowhere or traveling at v= 0 m/s for 7 seconds 10.) From 16s to 18 s: Traveling back 6m in 2 s or traveling at v= -3 m/s for 2 seconds 11.) From 18s to 20 s: Going nowhere or traveling at v= 0 m/s for 2 seconds 12.) From 20s to 25 s: Traveling back 2m in 5 s or traveling at v= 0.4 m/s for 5 seconds 13.) From 25s to 29 s: Going nowhere or traveling at v= 0 m/s for 4 seconds