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Unformatted text preview: PHYS-408 Fall 2008 Mastering Physics Assignment #2 Solutions Problem 15.6 (a) What volume of water has the same mass as 8.0 m 3 of ethyl alcohol? The density of water and ethyl alcohol is given in table 15.1, w = 1000 kg / m 3 and e = 790 kg / m 3 . The mass of the alcohol is M e = V e e = 8.0 m 3 ( ) 790 kg / m 3 ( ) = 6320 kg The mass of the water is the same, M w = 6320 kg , so M w = V w w V w = M w w = 6320 kg 1000 kg / m 3 = 6.32 m 3 (b) If this volume of water is in a cubic tank, what is the pressure at the bottom? If the tank is cubic, the depth is just h = 6.32 m 3 3 = 1.85 m The pressure at the bottom is then p = p + g w h = 101,300 Pa + 9.81 m / s 2 ( ) 1000 kg / m 3 ( ) 1.85 m ( ) = 119449 Pa This rounds off to p = 1.19 10 5 Pa Problem 15.10 A 20-cm-diameter circular cover is placed over a 10-cm-diameter hole that leads into an evacuated chamber. The pressure in the chamber is 20 kPa. (a) How much force is required to pull the cover off? The entire top of the cover is subject to 1 atm of pressure. The area is just A t = r 2 = 10 cm ( ) 2 = 0.10 m ( ) 2 = 0.0314 m 2 So the downward force is just F t = p a A t = 101,300 Pa ( ) 0.0314 m 2 ( ) = 3181 N The upward force has two aspects. The first is from the gas in the chamber acting through the 10 cm hole that is covered by the lid. This has an area A h = r 2 = 5...
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