problem14_66

University Physics with Modern Physics with Mastering Physics (11th Edition)

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Unformatted text preview: 14.66: The ball's volume is V= 4 3 4 r = (12.0 cm)3 = 7238 cm 3 3 3 As it floats, it displaces a weight of water equal to its weight. a) By pushing the ball under water, you displace an additional amount of water equal to 84% of the ball's volume or (0.84)(7238 cm 3 ) = 6080 cm 3 . This much water has a mass of 6080 g = 6.080 kg and weighs (6.080 kg)(9.80 m s 2 ) = 59.6 N, which is how hard you'll have to push to submerge the ball. b) The upward force on the ball in excess of its own weight was found in part (a): 59.6 N. The ball's mass is equal to the mass of water displaced when the ball is floating: (0.16)(7238 cm3 )(1.00 g cm3 ) = 1158 g = 1.158 kg, and its acceleration upon release is thus a= Fnet 59.6 N = = 51.5 m s 2 m 1.158 kg ...
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