8. Please answer part d and e, the previous parts are answered and the problem isn't incomplete Problem 8: In this problem you will measure the gravitational constant in a series of "observational experiments," making use ofNewton's law of gravitation and second law of motion as well as Kepler's third law of planetary motionPart (a) Newton measured the centripetal acceleration of the moon in its orbit around Earth by comparing the force Earth exerts on the moon withthe force Earth exerts on an apple. He obtained a value of a. = 2.7x103 m/s2. If Newton had taken the mass of Earth to be Mp = 6.01x1024 kg andthe mean distance between the centers of Earth and the moon to be RME = 3.86×10š m, what value would he have obtained for the gravitationalconstant, in units of N•m2/kg?Numeric : A numeric value is expected and not an expression.G =6.693 x L0Part (b) Since measuring the centripetal acceleration of an orbiting body is rather difficult, an alternative approach is to use the body's rotationalperiod instead. Enter an expression for the gravitational constant, in terms of the distance between Earth and the moon, RME, Earth's mass MF, andthe moon's period of rotation around Earth, T.Expression :G =Select from the variables below to write your expression. Note that all variables may not be required.B, y, T, 0, d, g, h, j, k, m, ME, n, P, RME,TPart (c) Using the expression you entered in part (b) and taking the rotational period of the moon to be T= 27.3 days, what value would Newtonhave calculated for the gravitation constant, in units of N•m2/kg²? Take ME = 6.01l×1024 kg and RME = 3.86×10³ m.Numeric : A numeric value is expected and not an expression.G =6,783x10-|Part (d) The gravitational constant may also be calculated by analyzing the motion of a rocket. Suppose a rocket is launched vertically from thesurface or Earth at an initial speed of v;. Its initial distance from the center of Earth is R;, the radius of Earth. Its peak distance, where its speed ismomentarily zero is, is Rç. For simplicity, ignore air resistance and Earth's rotation. Enter an expression for the gravitational constant, in terms ofVị, Rị, Rf, and Mg-MultipleChoice :1) v,? / ( 2 Mg (1/ R¡ - 1 / Rp ))2) v;2 / (2 MẸ ( 1 / Rf - 1 / R¡ ) )3) v,? R; / ( 2 MẸ )4) Vị / ( 2 MẸ ( 1 / R¡ - 1 / Rf ))5) v,? ( 1/ R; - 1/ Rf ) / ( 2 MẸ )6) v,? Rf / ( 2 MẸ )Part (e) Suppose a rocket is launched as described in part (d) with an initial speed of v; = 493 m/s and attains a peak altitude of H = 12.6 km abovethe surface of Earth. Taking Mp = 6.01×1024 kg and R; = 6.36x106 m, what is the measured value of the gravitational constant, in units ofN-m?/kg??Numeric : A numeric value is expected and not an expression.G =

d) The gravitational constant can be determined by using the conservation law of energy as, Here,…

Part (d) The gravitational constant may also be calculated by analyzing the motion of a rocket. Suppose a rocket is launched vertically from the surface or Earth at an initial speed of v;. Its initial distance from the center of Earth is R;, the radius of Earth. Its peak distance, where its speed is momentarily zero is, is Rf. For simplicity, ignore air resistance and Earth's rotation. Enter an expression for the gravitational constant, in terms of Vi, Rj, Rf, and Me- MultipleChoice : 1) v,? / ( 2 MẸ ( 1 / R¡ - 1 / Rf ) ) 2) v;? / ( 2 MẸ ( 1 / R -1/R¡ )) 3) v,? R; / ( 2 MẸ ) 4) vị / ( 2 MẸ ( 1 / R¡ - 1 / Rf )) 5) v? (1/R; - 1/Rp )/(2 MẸ ) 6) v? Rf/ ( 2 Mg ) Part (e) Suppose a rocket is launched as described in part (d) with an initial speed of v; = 493 m/s and attains a peak altitude of H = 12.6 km above the surface of Earth. Taking ME = 6.01x1024 kg and R; = 6.36x10° m, what is the measured value of the gravitational constant, in units of N-m?/kg?? Numeric : A numeric value is expected and not an expression. G =

Part (d) The gravitational constant may also be calculated by analyzing the motion of a rocket. Suppose a rocket is launched vertically from the surface or Earth at an initial speed of v;. Its initial distance from the center of Earth is R;, the radius of Earth. Its peak distance, where its speed is momentarily zero is, is Rf. For simplicity, ignore air resistance and Earth's rotation. Enter an expression for the gravitational constant, in terms of Vi, Rj, Rf, and Me- MultipleChoice : 1) v,? / ( 2 MẸ ( 1 / R¡ - 1 / Rf ) ) 2) v;? / ( 2 MẸ ( 1 / R -1/R¡ )) 3) v,? R; / ( 2 MẸ ) 4) vị / ( 2 MẸ ( 1 / R¡ - 1 / Rf )) 5) v? (1/R; - 1/Rp )/(2 MẸ ) 6) v? Rf/ ( 2 Mg ) Part (e) Suppose a rocket is launched as described in part (d) with an initial speed of v; = 493 m/s and attains a peak altitude of H = 12.6 km above the surface of Earth. Taking ME = 6.01x1024 kg and R; = 6.36x10° m, what is the measured value of the gravitational constant, in units of N-m?/kg?? Numeric : A numeric value is expected and not an expression. G =

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 45PQ: Figure P7.45 shows a picture of American astronaut Clay Anderson experiencing weightlessness on...

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Unreasonable Result A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight. (a) Calculate the mass of the mountain. (b) Compare the mountain's mass with that of Earth. (c) What is unreasonable about these results? (d) Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)
Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational. (a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child) (b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6.291011 m away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
A 200-kg object and a 500-kg object are separated by 4.00 m. (a) Find the net gravitational force exerted by these objects on a 50.0-kg object placed midway between them. (b) At what position (other than an infinitely remote one) can the 50.0-kg object be placed so as to experience a net force of zero from the other two objects?
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Figure P7.45 shows a picture of American astronaut Clay Anderson experiencing weightlessness on board the International Space Station. a. Most people have the misconception that a person in a spacecraft is weightless because he or she is no longer affected by gravity. Show that this premise cannot be true by computing the gravitational field of the Earth at an altitude of 200 km the typical altitude of a spacecraft in orbit. Compare this result with the gravitational field on the surface of the Earth. b. Why would astronauts in orbit experience weightlessness even if they are experiencing a gravitational field (and therefore a gravitational force)?
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A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00 of his weight. (a) Calculate the mass of the mountain. (b) Compare the mountain’s mass with that of Earth. (c) What is unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)
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The following objects are moving in uniform circular motion. Draw a free-body diagram for each object and identify the force responsible for the centripetal acceleration. Object 1. A person riding on the barrel-of-fun ride (Fig. 6.27, top) Object 2. The lead object in the laboratory set-up (Fig. 6.27, center) Object 3. A jogger running on a circular track (Fig. 6.27, bottom)
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