05_InstSolManual_PDF_Part32 - 5-32 Chapter 5 5.77 Set Up...

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5.77. Set Up: When the spring is stretched an amount x the spring force has magnitude kx and is directed to the right in the figure in the problem. The free-body diagram for the weight is given in Figure 5.77a. When the spring is compressed a distance the spring force has magnitude and is directed to the left. The free-body diagram for this case is given in Figure 5.77b. Figure 5.77 Solve: (a) gives and (b) gives and The acceleration is in the backward direction. 5.78. Set Up: The box and ball together have mass 35.0 kg. If the ball is at rest relative to the box it has the same acceleration as the box. For the ball use coordinates where is horizontal and to the right, in the direction of the acceleration. Solve: First find the acceleration of the box. The weight of the rock must accelerate a total mass of 45.0 kg. The box has acceleration (a) The free-body diagram for the ball is given in Figure 5.78. The string makes an angle
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Unformatted text preview: with the vertical. The ten-sion T has been resolved into its x and y components. Figure 5.78 (b) gives and gives Combining these two equations gives so (c) As the rock becomes very heavy its acceleration approaches g ; and f S 45°. tan f S 1 f 5 12.5° tan f 5 a g 5 2.18 m / s 2 9.80 m / s 2 1 mg cos f 2 sin f 5 ma . T sin f 5 ma . g F x 5 ma x T 5 mg cos f . T cos f 2 mg 5 g F y 5 ma y x y T cos f T sin f T mg f f a 5 1 10.0 kg 21 9.80 m / s 2 2 45.0 kg 5 2.18 m / s 2 . 1 x 5.23 m / s 2 , a x 5 2 k x m 5 2 1 250 N / m 21 0.0230 m 2 1.10 kg 5 2 5.23 m / s 2 . 2 k x 5 ma x g F x 5 ma x k 5 ma x 5 1 1.10 kg 21 2.50 m / s 2 2 0.0110 m 5 250 N / m kx 5 ma g F x 5 ma x x y mg mg n kx ( a ) x y n ( b ) k x a k x x 5-32 Chapter 5...
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  • Spring '07
  • Shoberg
  • Force, Mass, 2k, 2 mg, 5 2 m, 2.18 M

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