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garza (org87) - Homework 9 - Macdonald - (57960) This print-out should have 12 questions. Multiple-choice questions may continue on the next column...

#2. I have no idea how to derive the equation. I know Fy= -mg. Fx= i have no idea
garza (org87) – Homework 9 – Macdonald – (57960) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points A small, solid sphere oF mass m and radius r rolls without slipping along the track con- sisting oF slope and loop-the-loop with radius R at the end oF the slope. It starts From rest near the top oF the track at a height h , where h is large compared to r . P R m r θ h What is the minimum value oF h (in terms oF the radius oF the loop R ) such that the sphere completes the loop? The moment oF inertia For a solid sphere is 2 5 m r 2 . 1. h min = 1 . 8 ( R - r ) 2. h min = 2 . 7 ( R - r ) 3. h min = 2 . 5 ( R - r ) 4. h min = 3 . 7 ( R - r ) 5. h min = 2 . 8 ( R - r ) 002 (part 2 oF 2) 10.0 points What are the Force components on the sphere at the point P, which has coordinates ( - R, 0) iF we take the center oF the loop as origin, and iF h = 3 R ? 1. F y = - 1 2 mg , F x = + 10 7 2 R + r R - r mg 2. F y = - 2 mg , F x = + 10 7 2 R + r R - r mg 3. F y = - mg , F x = + 5 7 2 R + r R - r mg 4. F y = - mg , F x = + 10 7 2 R + r R - r mg 5. F y = - mg , F x = - 2 R + r R - r mg 003 10.0 points A solid steel sphere oF density 7 . 75 g / cm 3 and mass 0 . 3 kg spin on an axis through its center with a period oF 1 . 6 s. Given V sphere = 4 3 π R 3 , what is its angular momentum? Answer in units oF kg m 2 / s. 004 (part 1 oF 2) 10.0 points A student sits on a rotating stool holding two 1 . 8 kg masses. When his arms are extended horizontally, the masses are 0 . 74 m From the axis oF rotation, and he rotates with an angu- lar velocity oF 1 . 8 rad / sec. The student then pulls the weights horizontally to a shorter dis- tance 0 . 39 m From the rotation axis and his angular velocity increases to ω 2 . ω i ω f ±or simplicity, assume the student himselF plus the stool he sits on have constant com- bined moment oF inertia I s = 4 . 8 kg m 2 . ±ind the new angular velocity ω 2 oF the student aFter he has pulled in the weights. Answer in units oF rad / s. 005 (part 2 oF 2) 10.0 points When the student pulls the weights in, he perForms mechanical work — which increases the kinetic energy oF the rotating system.
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garza (org87) – Homework 9 – Macdonald – (57960) 2 Calculate the increase in the kinetic energy. Answer in units of J. 006 (part 1 of 2) 10.0 points A cylinder with moment of inertia 16 . 5 kg m 2 rotates with angular velocity 5 . 9 rad / s on a frictionless vertical axle. A second cylinder, with moment of inertia 40 . 2 kg m 2 , initially not rotating, drops onto the Frst cylinder and remains in contact. Since the surfaces are rough, the two eventually reach the same an- gular velocity. I 2 I 1 ω 0 Before ω After Calculate the Fnal angular velocity. Answer in units of rad / s. 007 (part 2 of 2) 10.0 points Show that energy is lost in this situation by calculating the ratio of the Fnal to the initial kinetic energy. 008 (part 1 of 2) 10.0 points Two objects of masses 10 kg and 18 kg are connected to the ends of a rigid rod (of negli- gible mass) that is 70 cm long and has marks every 10 cm, as shown. 10 kg 18 kg A B C D E F G H J 10 20 30 40 50 60 Which point represents the center of mass of the sphere-rod combination? 1. G 2. F 3. E 4. H 5. A 6. D 7. J 8. C 9. B 009 (part 2 of 2) 10.0 points The sphere-rod combination can be pivoted about an axis that is perpendicular to the plane of the page and that passes through one of the Fve lettered points. Through which point should the axis pass for the moment of inertia of the sphere-rod combination about this axis to be greatest? 1. C 2. G 3. F 4. A 5. E 6. H 7. J 8. D 9. B 010 10.0 points A weight (with a mass of 130 kg) is suspended from a point at the right-hand end of a uni- form boom with a mass of 62 kg . A horizontal cable at an elevation of 7 m is attached to the wall and to the boom at this same end point. The boom is also supported by a pivot (at the origin of the coordinate axes) on the same wall.
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