EAS208_HW01_090110_Solutions

EAS208_HW01_090110_S - EAS 208(Fall 2010 Homework#1 Solutions Problem 126 Suppose that you have just purchased a Ferrari F355 coupe and you want to

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EAS 208 (Fall 2010) Homework #1 – Solutions Problem 12–6 Suppose that you have just purchased a Ferrari F355 coupe and you want to know whether you can use your set of SAE (U.S. Customary unit) wrenches to work on it. You have wrenches with widths 1 4 wi n 1 2 in = , , 3 4 in , and 1 , and the car has nuts with dimensions , 10 , 15 , , and . Defining a wrench to fit if w is no more than larger than , which of your wrenches can you use? in 5 nm m = mm mm 20 mm 25 mm 2% n Answer: Convert metric wrench widths to inches and check if they satisfy the tolerance criteria. n Wrench width SI unit U.S. Customary unit Tolerance 5 mm 1 5 0.1968 25.4 in mm in mm = 0.1968 0.25 100 27.03% 0.1968 ⎛⎞ =− ⎜⎟ ⎝⎠ 10 mm 1 10 0.3937 25.4 in mm in mm = 0.3937 0.50 100 27.00% 0.3937 15 mm 1 15 0.5905 25.4 in mm in mm = 0.5905 0.50 100 15.33% 0.5905 = 20 mm 1 20 0.7874 25.4 in mm in mm = 0.7874 0.75 100 4.75% 0.7874 = 25 mm 1 25 0.9842 25.4 in mm in mm = 0.9842 1.00 100 1.60% 0.9842 OK A negative percentage implies that the metric nut is smaller than the SAE wrench, while a positive percentage means that the metric nut is larger than the SAE wrench. The only wrench that can be used, satisfying the tolerance criteria of fit, is the 1 wrench that fits the 25 nut. The other wrenches cannot be used. 2% in mm 1
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Problem 12–30 At a point between the earth and the moon, the magnitude of the force exerted on an object by the earth’s gravity equals the magnitude of the force exerted on the object by the moon’s gravity. What is the distance from the center of the earth to that point to three significant digits? The distance from the center of the earth to the center of the moon is , and the radius of the earth is . The radius of the moon is 1738 , and the acceleration due to gravity at its surface is 383,000 km 6370 km km 2 1.62 m s . Answer: The acceleration due to gravity at a distance r from the center of a planet in terms of the acceleration due to gravity at surface level of the planet R is: 2 2 R ag r = At a point between the earth and the moon, where the magnitude of the force exerted on an object by the earth’s gravity equals the magnitude of the force exerted on the object by the moon’s gravity (see Figure below), the gravitational accelerations are the same: 2
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() 2 2 2 2 m E Em R R ag g r dr == 22 2 2 6370 1738 9.81 1.62 383,000 mk m m k m sr s km r ⇒= 344,770 345,000 rk m = k m 3
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Problem 13–12 The acceleration (in 2 m s ) of point relative to point
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This document was uploaded on 10/27/2011 for the course EAS 208 at SUNY Buffalo.

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EAS208_HW01_090110_S - EAS 208(Fall 2010 Homework#1 Solutions Problem 126 Suppose that you have just purchased a Ferrari F355 coupe and you want to

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