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10_InstSolManual_PDF_Part23 - and its final height is...

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10.64. Set Up: The free-body diagram for the drawbridge is given in Figure 11.64. and are the components of the force the hinge exerts on the bridge. Figure 10.64 Solve: (a) with the axis at the hinge gives and (b) gives gives and The hinge force has magnitude and is directed at above the horizontal. (c) For an axis at the hinge, and gives 10.65. Set Up: Take upward and at the ground. The center of mass of the vine is 4.00 m from either end. Treat the motion in three parts: (i) Jane swinging to where the vine is vertical. Apply conservation of energy. (ii) The inelastic collision between Jane and Tarzan. Apply conservation of angular momentum. (iii) The motion of the combined object after the collision. Apply conservation of energy. The vine has and Jane has so the system of Jane plus vine has Solve: (a) The initial and final positions of Jane and the vine for the first stage of the motion are sketched in Fig- ure 10.65a. The initial height of the center of the vine is
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Unformatted text preview: and its final height is Con-servation of energy gives so Figure 10.65 5.00m h vine,i h vine,f 5 4.00m m Jane Initial 1.50m 1.50m m vine 4.00m m vine m Jane y 5 Final ( a ) K i 5 U i 1 K i 5 U f 1 K f . h vine, f 5 4.00 m. h vine, i 5 6.50 m I tot 5 A 1 3 m vine 1 m Jane B l 2 . I 5 m Jane l 2 , I 5 1 3 m vine l 2 y 5 1 y a 5 g t I 5 1 45,000 N 21 7.0 m 2 cos 37° 3.0 3 10 5 kg # m 2 5 0.839 rad / s 2 g t 5 I a I 5 1 3 mL 2 5 1 3 1 45,000 N 9.80 m / s 2 2 1 14.0 m 2 2 5 3.0 3 10 5 kg # m 2 . g t 5 w 1 7.0 m 21 cos 37° 2 T S 0. 20.7° 1.27 3 10 5 N u 5 20.7°. tan u 5 H v H h H 5 " H h 2 1 H v 2 5 1.27 3 10 5 N. H v 5 w 5 4.50 3 10 4 N. g F y 5 H h 5 T 5 1.19 3 10 5 N. g F x 5 T 5 2 w cos 37° sin 37° 5 1 45,000 N 2 tan 37° 5 1.19 3 10 5 N 2 w 1 7.0 m 21 cos 37° 2 1 T 1 3.5 m 21 sin 37° 2 5 g t 5 x y w 3.5m 7.0m 37 ° T H v H h Axis 1 3.5m H h H v Dynamics of Rotational Motion 10-23...
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