Hw 7 Solutions

# I is the pressure inside and a is the area of the lid

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i is the pressure inside, and A is the area of the lid. Recalling that 1N/m 2 = 1 Pa, we obtain 5 4 4 2 480 N 1.0 10 Pa 3.8 10 Pa. 77 10 m i o F p p A = = × = × × P9.- Let the volume of the expanded air sacs be V a and that of the fish with its air sacs collapsed be V . Then 3 3 fish fish fish 1.08 g/cm and 1.00 g/cm w a m m V V V ρ ρ = = = = + where ρ w is the density of the water. This implies ρ fish V = ρ w ( V + V a ) or ( V + V a )/ V = 1.08/1.00, which gives V a /( V + V a ) = 7.4%. P10.- The pressure p at the depth d of the hatch cover is p 0 + ρ gd , where ρ is the density of ocean water and p 0 is atmospheric pressure. The downward force of the water on the hatch cover is ( p 0 + ρ gd ) A , where A is the area of the cover. If the air in the submarine is at atmospheric pressure then it exerts an upward force of p 0 A . The minimum force that must be applied by the crew to open the cover has magnitude F = ( p 0 + ρ gd ) A p 0 A = ρ gdA = (1024 kg/m 3 )(9.8 m/s 2 )(100 m)(1.2 m)(0.60 m) = 7.2 × 10 5 N. P11.- (a) At depth y the gauge pressure of the water is p = ρ gy , where ρ is the density of the water. We consider a horizontal strip of width W at depth y , with (vertical) thickness

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dy , across the dam. Its area is dA = W dy and the force it exerts on the dam is dF = p dA = ρ gyW dy . The total force of the water on the dam is ( ) ( ) ( )( ) 2 0 2 3 3 2 9 1 2 1 1.00 10 kg m 9.80m s 314m 35.0m 1.88 10 N. 2 D F gyW dy gWD ρ ρ = = = × = × P12.- (a) The force on face A of area A A due to the water pressure alone is ( ) ( ) ( ) 3 2 3 3 2 6 (2 ) 2 1.0 10 kg m 9.8m s 5.0m 2.5 10 N. A A A w A A w F p A gh A g d d ρ ρ = = = = × = × Adding the contribution from the atmospheric pressure, F 0 = (1.0 × 10 5 Pa)(5.0 m) 2 = 2.5 × 10 6 N, we have 6 6 6 0 ' 2.5 10 N 2.5 10 N 5.0 10 N. A A F F F = + = × + × = × (b) The force on face B due to water pressure alone is ( ) ( ) ( ) 3 2 3 3 3 2 avg 6 5 5 5 1.0 10 kg m 9.8m s 5.0m 2 2 2 3.1 10 N.
• Fall '11
• Robbert

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