3. When the first railroad was built from the east coast to the west coast across India, the surveyors found that there was an error in their measurements. They later figured out the reason was that their plumb bobs did not point exactly straight down towards the center of the Earth. The cause of this error was the presence of the Himalayan mountains to the north. This error added up when repeated many times over hundreds of miles. Suppose that the railroad was built about 100 km south of the mountains, and the estimated mass of the Himalayas is 3 x 10¹7 kg. What angle would the plumb bob be deflected from "vertical" (toward the center of the Earth) by the gravitational attraction of the Himalayas?

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2. The mass of the Earth is approximately 80 times the mass on the Moon. Let M be the mass of the Moon and 80M
be the mass of the Earth. The distance between the Earth and the Moon is d.
a.
During one of the Apollo Moon trips, the
spacecraft of mass m is at the position shown.
Determine the net force on the spacecraft in
terms of m, M, and d and physical constants.
Start by drawing the free body diagram showing
the forces on the spacecraft.
+y
m
+x
d
M
Moon
d
80M
3. When the first railroad was built from the east coast to the west coast across India, the surveyors found that there
was an error in their measurements. They later figured out the reason was that their plumb bobs did not point
exactly straight down towards the center of the Earth. The cause of this error was the presence of the Himalayan
mountains to the north. This error added up when repeated many times over hundreds of miles. Suppose that the
railroad was built about 100 km south of the mountains, and the estimated mass of the Himalayas is 3 x 10¹7 kg.
What angle would the plumb bob be deflected from "vertical" (toward the center of the Earth) by the gravitational
attraction of the Himalayas?
Earth
Transcribed Image Text:2. The mass of the Earth is approximately 80 times the mass on the Moon. Let M be the mass of the Moon and 80M be the mass of the Earth. The distance between the Earth and the Moon is d. a. During one of the Apollo Moon trips, the spacecraft of mass m is at the position shown. Determine the net force on the spacecraft in terms of m, M, and d and physical constants. Start by drawing the free body diagram showing the forces on the spacecraft. +y m +x d M Moon d 80M 3. When the first railroad was built from the east coast to the west coast across India, the surveyors found that there was an error in their measurements. They later figured out the reason was that their plumb bobs did not point exactly straight down towards the center of the Earth. The cause of this error was the presence of the Himalayan mountains to the north. This error added up when repeated many times over hundreds of miles. Suppose that the railroad was built about 100 km south of the mountains, and the estimated mass of the Himalayas is 3 x 10¹7 kg. What angle would the plumb bob be deflected from "vertical" (toward the center of the Earth) by the gravitational attraction of the Himalayas? Earth
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