10_InstSolManual_PDF_Part6 - 10-6 Chapter 10 10.15 Set Up...

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10.15. Set Up: The free-body diagram for the ball is shown in Figure 10.15. Use the coordinates shown. Take clockwise torques to be positive. For a hollow sphere, Figure 10.15 Solve: (a) Apply to the motion of the center of mass: Apply to the rotation about the center of mass: and Combining these two equations to eliminate T gives and (b) (c) Reflect: The tension T is less than the weight and the sphere accelerates downward. 10.16. Set Up: Let be down the incline and let the shell be turning in the positive sense of rotation. Apply to the translational motion of the center of mass and to the rotation about the center of mass. The free-body diagram for the shell is given in Figure 10.16. From Table 9.2, Figure 10.16 Solve: gives gives With this becomes Combining the equations gives and The friction is static since there is no slipping at the point of contact. (b) The acceleration is independent of
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Unformatted text preview: m and doesn’t change. The friction force is proportional to m so will double; f 5 9.66 N. f 5 2 3 ma cm 5 2 3 1 2.00 kg 21 3.62 m / s 2 2 5 4.83 N. a cm 5 3 g sin b 5 5 3 1 9.80 m / s 2 21 sin 38.0° 2 5 5 3.62 m / s 2 . mg sin b 2 2 3 ma cm 5 ma cm f 5 2 3 ma cm . a 5 a cm / R fR 5 A 2 3 mR 2 B a . g t 5 I a mg sin b 2 f 5 ma cm . g F x 5 ma x a n mg sin b mg cos b b b mg a cm f I cm 5 2 3 mR 2 . g t 5 I a g F S 5 m a S 1 x w 5 Mg 5 122.5 N a 5 a cm R 5 5.88 m / s 2 0.176 m 5 33.4 rad / s 2 T 5 2 3 Ma cm 5 2 3 1 12.5 kg 21 5.88 m / s 2 2 5 49.0 N a cm 5 3 5 g 5 5.88 m / s 2 . Mg 2 2 3 Ma cm 5 Ma cm T 5 2 3 Ma cm . TR 5 A 2 3 MR 2 B 1 a cm R 2 TR 5 I cm a . g t 5 I a Mg 2 T 5 Ma cm . g F y 5 ma y T a y x Mg a cm 1 R 5 0.176 m. a cm 5 R a . I cm 5 2 3 MR 2 . 10-6 Chapter 10...
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  • Spring '07
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