An astronaut working on the Moon tries to determine the gravitational constant G by throwing a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the Moon has a density pof 3340 kg/m and a radius Rof 1740 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: R 47G mp. 3 E (2) R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G 8n pR? R (3) R+h (c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?
An astronaut working on the Moon tries to determine the gravitational constant G by throwing a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the Moon has a density pof 3340 kg/m and a radius Rof 1740 km. (a) Show with (1) that the potential energy of the rock at height h above the surface is given by: R 47G mp. 3 E (2) R+h (b) Next, show that the gravitational constant can be determined by: -1 3 v2 G 8n pR? R (3) R+h (c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:An astronaut working on the Moon tries to determine the gravitational constant G by throwing
a Moon rock of mass m with a velocity of v vertically into the sky. The astronaut knows that the
Moon has a density pof 3340 kg/m³ and a radius R of 1740 km.
(a) Show with (1) that the potential energy of the rock at height h above the surface is given by:
R
47G
mp-
3
E
(2)
R+h
(b) Next, show that the gravitational constant can be determined by:
-1
3 v2
G
8n pR?
R
(3)
R+h
(c) What is the resulting G if the rock is thrown with 30 km/h and reaches 21.5 m?
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