hw01 statics - STATICS AND MECHANICS OF MATERIALS, 2nd...

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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 4 (a) ±² 16 2 9.181 10 209.4 lb 3960 5280 29,028 W u ....................................... Ans. (b) 16 2 9.181 10 190.3 lb 3960 200 5280 W u ³u ªº ¬¼ ........................................ Ans. 1-12 A space traveler weighs 800 N on earth. A planet having a mass of 5(10 25 ) kg and a diameter of 30(10 6 ) m orbits a distant star. Determine the weight W of the traveler on the surface of this planet. SOLUTION 2 2 1 r m Gm W Therefore on the surface of the earth where 24 5.976 10 kg e m u and 6370 km r 24 2 3 5.976 10 800 6370 10 Gm u u 92 5.432 10 N m /kg Gm ´ u µ Then on the surface of the planet where 25 51 0 k g m u and 6 15 10 m r u ± ² 5 2 6 5.432 10 5 10 1207 N 15 10 W ´ uu u ......................................... Ans. 1-13 The planet Jupiter has a mass of 1.302(10 26 ) slug and a visible diameter (top of the cloud layer) of 88,700 mi. Determine the gravitational acceleration g (a.) At a point 100,000 miles above the top of the clouds. (b.) At the top of the cloud layers. SOLUTION 2 2 1 r m Gm W (a) 82 6 2 3.439 10 1.302 10 44,350 100,000 5280 m Wm g ´ 2 7.71 ft/s g ................................................................. Ans. (b) 6 2 3.439 10 1.302 10 44,350 5280 m g ´ u 2 81.7 ft/s g ................................................................ Ans. 1-14 The planet Saturn has a mass of 5.67(10 26 ) kg and a visible diameter (top of the cloud layer) of 120,000 km. The weight W of a planetary probe on earth is 4.50 kN. Determine (a.) The weight of the probe when it is 600,000 km above the top of the clouds. (b.) The weight of the probe as it begins its penetration of the cloud layers. SOLUTION 2 2 1 r m Gm W
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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 5 Therefore on the surface of the earth where 24 5.976 10 kg e m u and 6370 km r ±² 24 2 3 5.976 10 4500 6370 10 Gm u u 82 3.055 10 N m /kg Gm ³ u ´ (a) ± ² 6 2 3 3.055 10 5.67 10 39.8 N 60,000 600,000 10 W ³ uu ªº µu ¬¼ ..................................... Ans. (b) ± ² 6 2 3 3.055 10 5.67 10 4810 N 60,000 10 W ³ u ...................................... Ans. 1-15 The first U.S. satellite, Explorer 1 , had a mass of approximately 1 slug. Determine the force exerted on the satellite by the earth at the low and high points of its orbit, which were 175 mi and 2200 mi, respectively, above the surface of the earth. SOLUTION 12 2 Gm m F r 3 2 3.439 10 4.095 10 1 29.5 lb 3960 175 5280 F ³ ................................... Ans. 3 2 3.439 10 4.095 10 1 13.31 lb 3960 2200 5280 F ³ .................................. Ans. 1-16 A neutron star has a mass of 2(10 30 ) kg and a diameter of 10 km. Determine the gravitational force of attraction on a 10-kg space probe (a.) When it is 1000 km from the center of the star. (b.) At the instant of impact with the surface of the star. SOLUTION 2 Gm m F r ± ² 11 30 9 2 3 6.673 10 2 10 10 1.335 10 N 1000 10 F ³ u u ............................... Ans. ± ² 11 30 13 2 3 6.673 10 2 10 10 5.34 10 N 51 0 F ³ u u ............................... Ans. 1-17 Determine the weight W , in U.S. customary units, of a 75-kg steel bar under standard conditions (sea level at a latitude of 45 degrees). SOLUTION ± ² ± ² 75 9.81 735.75 N 0.2248 lb/N 165.4 lb Wm g ...................... Ans.
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STATICS AND MECHANICS OF MATERIALS, 2 nd Edition RILEY, STURGES AND MORRIS 8 1-31 In the dimensionally homogeneous equation I Mc A P ± V is a stress, A is an area, M is a moment of a force, and c is a length. Determine the dimensions of P and I . SOLUTION ²³ 22 2 2 ML T L MP LT I L §· ± ¨¸ ©¹ Therefore 2 MM L PL F LT T § · ¨ ¸ © ¹ ............................................... Ans.
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hw01 statics - STATICS AND MECHANICS OF MATERIALS, 2nd...

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