HW_08_S - Ph1a Solutions 8 Chefung Chan([email protected]

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Ph1a Solutions 8 Chefung Chan ([email protected]) 21 November 2004 Each homework problem is worth 5 points. Please disregard the point values listed on the problem itself. Use these instead. 8.1 Serway 12.24(6th)/12.22(5th) (5 points) 8.1.a (5 points) For the bricks to stay on the ledge, their combined center of mass must be directly above the ledge. We define x = 0 at the corner of the ledge and the overhang of the bottom brick as x 0 . The centers of mass of the two bricks are: CM top = x - L/ 2 CM bottom = x 0 - L/ 2 CM combined = 1 2 (CM top + CM bottom ) = 1 2 ( x + x 0 - L ) The conditions for support are: CM top x 0 x - L/ 2 x 0 CM combined 0 1 2 ( x + x 0 - L ) 0 x - x 0 L/ 2 x + x 0 L x 3 4 L 8.2 FP3 (5 points) 8.2.a (2 points) The volume flow rate must be constant which implies ( vA ) hose = ( vA ) end , where v is the speed of the fluid and A is the cross sectional area. Since A end = 1 / 2 A hose , v end = 2 v hose = 2 * 5 m / s = 10 m / s. 8.2.b (3 points) First, change units to SI units: P end = 1 atm = 1 × 10 5 Pa, P hose = 0 . 5 atm = 5 × 10 4 Pa. Bernoulli’s equation gives: P end + 1 / 2
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