Not yet answered Marked out of 12.50 Question 3 Assume that the earth is a unifo

Question

Not yet answered Marked out of 12.50 Question 3 Assume that the earth is a uniform density spherical mass. (This assumption is not correct but we will use it for simplicity in working the problem.) The deepest hole drilled into the earth's surface went to a depth of 40,230 ft (Wikipedia.org). Imagine that this hole was straight toward the center of the earth and that a small 300 kg spherical mass was dropped into the hole and ended up at the very bottom of it. What would be the weight of the spherical mass at that location? Round your answer to the nearest hundredth decimal place and give your answer in the form "a.bc x 10 (y)" N. nswer

Explanation / Answer

acceleration due to gravity at a depth d below earth surface is

g_d = g * (1 - d / radius of earth)

so,

at depth of 40,230 ft or 12262.104 m acceleration due to gravity will be

radius of earth = 6371000 m

g_d = 9.8 * (1 - 12262.104 / 6371000)

g_d = 9.7811 m/s^2

weight = mass * g_d

mass = 300 kg

weight = 300 * 9.7811

weight = 2934.33 N

weight at depth of 40230 ft will be 2934.33 N or 2.93 * 10^3 N5

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