College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Background: GmM Newton formulated the Universal Law of Gravitation: F = R2 where, the gravitational force between two masses. the gravitational constant, G = 6.67 x 101' N- m²/kg? the mass of one object mass of other object distance between the center of the objects F G = m = M = R = Also, we learned that weight, w =mg. Equating weight with Newton's Law of Gravitation we get: mg = GmM or canceling m: R2 GM g = R2 This can be used to calculate the acceleration of gravity on any planet/object/body. Objective: Investigate several phenomena using Newton's Universal Law of Gravitation. Understand the difference between accuracy and precision. Procedure: Perform the indicated calculations. The following information can be used for the calculations. | 1.50 x 10" m 6.38 x 10 m 1.74 x 10° m 12,000 m 6.3 x 10" m Mass of Sun 1.99 x 100 kg 5.98 x 10²ª kg 7.36 x 1022 kg 2 x 100 kg 1.90 x 107 kg Earth-Sun distance Radius of Earth Radius of Moon Radius of neutron star Earth-Jupiter distance (in-line) Mass of Earth Mass of Moon Mass of neutron star Mass of Jupiter Error and Uncertainty: All measurements contain error and thus uncertainty. We can calculate errors depending on the nature of the experiment. We define two main types of uncertainty: Precision is how well independent measurements (Ej and E2) match. Precision can be |E - E| quantified using the formula: Percent Difference = x100 (E, + E,)/2 Percent difference is used when there is not an accepted value; it is used to compare two independent quantities. Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can be quantified using the formula: Percent Error =|A-E/A×100 Percent error is used to compare a quantity/measurement to an accepted value.
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Transcribed Image Text:Background: GmM Newton formulated the Universal Law of Gravitation: F = R2 where, the gravitational force between two masses. the gravitational constant, G = 6.67 x 101' N- m²/kg? the mass of one object mass of other object distance between the center of the objects F G = m = M = R = Also, we learned that weight, w =mg. Equating weight with Newton's Law of Gravitation we get: mg = GmM or canceling m: R2 GM g = R2 This can be used to calculate the acceleration of gravity on any planet/object/body. Objective: Investigate several phenomena using Newton's Universal Law of Gravitation. Understand the difference between accuracy and precision. Procedure: Perform the indicated calculations. The following information can be used for the calculations. | 1.50 x 10" m 6.38 x 10 m 1.74 x 10° m 12,000 m 6.3 x 10" m Mass of Sun 1.99 x 100 kg 5.98 x 10²ª kg 7.36 x 1022 kg 2 x 100 kg 1.90 x 107 kg Earth-Sun distance Radius of Earth Radius of Moon Radius of neutron star Earth-Jupiter distance (in-line) Mass of Earth Mass of Moon Mass of neutron star Mass of Jupiter Error and Uncertainty: All measurements contain error and thus uncertainty. We can calculate errors depending on the nature of the experiment. We define two main types of uncertainty: Precision is how well independent measurements (Ej and E2) match. Precision can be |E - E| quantified using the formula: Percent Difference = x100 (E, + E,)/2 Percent difference is used when there is not an accepted value; it is used to compare two independent quantities. Accuracy is how close a measurement (E) is to an accepted value (A). Accuracy can be quantified using the formula: Percent Error =|A-E/A×100 Percent error is used to compare a quantity/measurement to an accepted value.
1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star. 2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, the GM orbital velocity (speed) of an object can be shown to be: v = Where M is the R mass of the body being orbited and R is the average distance from the body. A) Calculate Earth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C) Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits the Sun in approximately a circle every 365 days. Speed = Distance/Time. Distance = the circumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D) Compare the orbital velocities (speeds) from Parts A and C by calculating the percent difference of the two velocities and comment (are they about the same?). Earth M (Sun) 3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitational pull on humans is significant, and thus affects our life. A) Calculate the gravitational pull from Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B) Calculate the gravitational pull from a skyscraper on a human walking through any downtown, or city center (Assume a skyscraper has a mass of 1.2 x 10° kg, and the distance between the center of masses is 175 m). C) Calculate the pull from a large cliff (M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and C than the answer in part A? Comment on these results. m = 70 kg A) R M (Jupiter) m = 70 kg B) M (skyscraper) m = 70 kg C) R. M (cliff)
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Transcribed Image Text:1. Calculate the acceleration of gravity on A) the Earth. B) the Moon. C) a neutron star. 2. Forces cause accelerations, and thus velocity. Using Newton's Law of Gravitation, the GM orbital velocity (speed) of an object can be shown to be: v = Where M is the R mass of the body being orbited and R is the average distance from the body. A) Calculate Earth's orbital velocity around the Sun. B) How fast is Earth traveling in m.p.h.? C) Calculate Earth's orbital velocity using a second method. (Hint: The Earth orbits the Sun in approximately a circle every 365 days. Speed = Distance/Time. Distance = the circumference of Earth's orbit = 2rR and Time is number of seconds in a year.) D) Compare the orbital velocities (speeds) from Parts A and C by calculating the percent difference of the two velocities and comment (are they about the same?). Earth M (Sun) 3. Astrologers claim that when Jupiter is 'lined-up' with the Earth and Sun, its gravitational pull on humans is significant, and thus affects our life. A) Calculate the gravitational pull from Jupiter on a human (m=70 kg) when Jupiter is 'in-line' with the Earth and Sun. B) Calculate the gravitational pull from a skyscraper on a human walking through any downtown, or city center (Assume a skyscraper has a mass of 1.2 x 10° kg, and the distance between the center of masses is 175 m). C) Calculate the pull from a large cliff (M=8.8 x 107 kg and R=14 m). D) How many times bigger are the answers in B and C than the answer in part A? Comment on these results. m = 70 kg A) R M (Jupiter) m = 70 kg B) M (skyscraper) m = 70 kg C) R. M (cliff)
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