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SOLUTIONS TO EXERCISE 27
(a) The distance from the Moon to the closest edge of Earth's surface is 384,000,000 - 6,378,000 = 377,622,000 m 6.67 * 10^(-11) m^3 kg^(-1) s^(-2) * 7.36 * 10^22 kg So acceleration a = GM/r2 = ----------------------------------------------------- (377,622,000 m)^2 = 0.000035 m/s^2. (b) The distance from the Moon to the farthest edge of Earth's surface is 384,000,000 + 6,378,000 = 390,378,000 m 6.67 * 10^(-11) m^3 kg^(-1) s^(-2) * 7.36 * 10^22 kg So acceleration a = GM/r2 = ----------------------------------------------------- (390,378,000 m)^2 = 0.000033 m/s^2. (c) The difference between these two accelerations is 0.000002 m/s^2, or 2 millionths of a meter per second squared. Since Earth's gravitational acceleration is about 10 m/s^2, this "tidal differential" is 1/5,000,000 the strength of Earth's gravity at Earth's surface. This "tidal differential," as you know from the text, is responsible for our ocean tides here on Earth. The difference in acceleration seems tiny - but it works over the entire surface of Earth as our planet rotates; so the amount of total mass that's moved is tremendous. As a result, ocean tides carry a lot of power compared to typical human consumption levels. Can we harness that tidal power for use in our homes and businesses? At this time, the technology is promising. |