1112CPIS1_test2_sol_student_version - S and 2 a hemisphere...

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Mid-term Test 2 Suggested solutions Section A: Multiple Choice Questions (45 marks) E D E C C D B C C Section B: Long Questions (55 marks) 1. (A) (B) (a) mg = kx k = (75kg)(9.8m/s 2 )/4.0 x 10 -2 m = 1.84 x 10 4 N/m (b) (c) 2. Since the solid S has symmetry about the z axis, its center of mass must lie along the z axis so that x CM = y CM = 0. We may regard the solid S to be composed of two parts: 1. a solid cube C with edge length d and density ρ at the same position as
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Unformatted text preview: S , and 2. a hemisphere H with radius r and density -at the same position as the hole in S . The cube C has mass m C = d 3 and its center of mass lies on the z-axis with z c oordinate z C = d /2 (because of its symmtery). In addition, the hemisphere H has mass m H = ½(4/3 π r 3 ) and its center of mass lies on the z-axis with z coordinate z H = d - 3/8 r . Therefore, the center of mass of the solid S is located at: 1...
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