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201 PHYSICS Lab 7. Gravitation Objectives: 1) To demonstrate an understanding of Newton s Universal Law of Gravitation, 2) To apply the idea of centripetal acceleration and artificial gravity to a rotating object by designing a space station, and 3) To determine if the movie Armaggedon realistically depicts artificial gravity for the Mir space station. Section 1: Newton s Universal Law of Gravitation Chapter 6 in your text outlines the law of gravitation. Basically, everything with mass is attracted to everything else with mass. The Law: If two objects of masses m1 and m2 are separated by a distance, r, then the attractive gravitational force is given by FG = Gm1m2 where G is a universal constant equal to 6.67 x 10-11 N m2/kg2. r2 1. Determine the order of magnitude (closest power of ten, reported simply as 10x without any prefix numbers) of the gravitational force that you exert on the classmate seated closest to you. To determine your mass, calculate it based on your weight in pounds (using the conversion factors in your text). You may use the bathroom scale in the lab to determine your weight in pounds. 2. Use the Law of Gravitation to calculate (to two or three sig figs) the gravitational force that you exert on the Earth and the Earth on you. Think carefully about the values for m1 and m2 as well as for r in the equation. A rough sketch should prove helpful. Compare this value to your weight, using W = mg. 3. Use the expression derived on the prelab to calculate the acceleration of gravity on the surface of a planet of your choice in our solar system. Planetary data can be found online. 4. Away from the surface of the Earth, the value for r must be adjusted accordingly from the radius of the planet to the total distance of the object from the center of the Earth. In 1960, US Air Force Captain Joseph Kittinger entered the record books when he stepped off the gondola of a helium balloon at an altitude of 31,330 meters (Note from Example 6-4 that Mt. Everest is about 29,000 feet high). Calculate the gravitational acceleration that Captain Kittinger experienced at that altitude. Have your work checked before proceeding to Section 2. Part Two: Centripetal Acceleration and Artificial Gravity 1. a) Discuss (in writing) question 18 from Chapter 5. Calculate the rotation rate (in rev/min) and tangential velocity in the shell (in m/s) for a space station diameter of 120 m that provides a simulated gravitational acceleration of 3.00 m/s2. b) Work problem 48 in Ch 5. Check your answers with your instructor. 2. Suppose that you are part of an engineering team who has been given the task of designing a space station which spins about its axis in order to create artificial gravity. The station will be home for approximately 50 scientists and space explorers plus a staff of 30 cooks, cleaners, engineers, communications experts, and general support staff. Each of the 80 people aboard will have their own or share quarters but they will all share a dining hall and recreation areas. There must also be several laboratories. The 27 PHYSICS 201 Lab 7. Gravitation living and working quarters will be located in the outer ring, with the engines and such in the center. Your job is to design the station with a rotation rate less than 4 rpm based on the given information. Determine the dimensions of the station. This means you must decide on the approximate size of the labs, living quarters, dining and recreational areas in order to arrive at a reasonable size for the station. You cannot just choose them arbitrarily. Do some calculations based on reasonable choices for the sizes of living quarters, labs, etc. Note that the total area for the labs and living spaces is NOT the area of a circle. (Refer to the figures below.) Think carefully about how to determine the floor area of your ship. Also note that the centripetal force (which provides a feeling of gravity) depends on the distance from the center, so not every part of the station will be able to provide the feeling of being on earth, especially if you decide to have more than one story on your station. Determine the rotation rate (in rev/minute) and the tangential speed such that the artificial gravity will be equal to 9.8 m/s2 as experienced on Earth for the outer ring of the station. If your values are unreasonably high, you should make the necessary changes and recalculate. The Report: You are NOT required to submit a Lab Write lab report. Submit a summary of Section 2, part 2 consisting of the following: 1. Draw sketches (2-D; as well as 3-D) and write about a paragraph-length description of the station. 2. Write a brief rationale for the dimensions you chose. 3. Download, complete and submit the Mir Artificial Gravity analysis (PDF file). 28

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