HW1-2Sol - Oregon State University Physics 202 HW1-2...

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Oregon State University Physics 202 , Winter 2010 HW1-2 (due Jan 15 at 5:00 p.m.) Page 1 Oregon State University Physics 202 Winter Term, 2010 HW1-2 Solutions 1. Pure water and then oil (which donʼt mix) are poured into a U-shaped tube, open at both ends. The liquids come to equilibrium as shown here. What is the oilʼs density? The key to this problem is to realize that the pressures at points A and B are equal: P A = P B Any two points at the same level (same “altitude”) in the same incompressible static fl uid are at equal pressure. Also, both the surface pressures above each respective column of uid are just atmospheric pressure, P atm . And by the equation for pressure at depth in a static fl uid, we know that P A = P atm + ρ oil gh oil and P B = P atm + ρ water gh r water Substituting, we have this: P atm + ρ oil gh oil = P atm + ρ water gh r water Just solve that for ρ oil . Subtract P atm from both sides: ρ oil gh oil = ρ water gh water Divide both sides by g : ρ oil h oil = ρ water h water Divide both sides by h oil : ρ oil = ( i ρ water h water )/ h oil Plug in the numbers: ρ oil = (1000)(.172 – .0625)/.172 = 637 kg/m 3 The density of the oil is 637 kg/m 3 . 17.2 cm 6 . 25 c m water oil P B P A
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Oregon State University Physics 202 , Winter 2010 HW1-2 (due Jan 15 at 5:00 p.m.) Page 2 2. A raft is made of 12 identical logs lashed together. Each log is 36.0 cm in diameter, 7.25 m long, and has a density of 750 kg/m 3 . How many 60-kg persons can the raft hold (fl oating in pure water) while still keeping everyoneʼs feet dry? Buoyancy is a matter of comparing weights. When an object fl oats, its entire weight, W obj , is supported (op- posed) by the buoyant force, F B , which is the weight of the fl uid displaced ( W ). That is: W obj = F B = W (But W obj = F B is true only if the object is fl oating . If it is not fl oating—i.e. if itʼs sitting at the bottom of the uid—then F B = W is still true, but itʼs not supporting the entire W obj ; that is, W obj > F B .) In this problem, W obj = W raft + W people . And we can calculate the buoyant force, the weight of the fl uid displaced: W = ( ρ water )( V water ) g = ( ρ water )( V raft ) g , because in order to get the maximum buoyant force, the raft logs must displace the maximum amount of water—be completely immersed. But V raft = 1 f 2 V log , so W = ( ρ water )(12 V log ) g So ( ρ water )(12 V log ) g = W raft + W people Likewise, W raft = f ( ρ log )( V raft ) g = ( ρ log )( 2 V log ) g And W people = n ( mg ), where n is the number of persons and m is the mass of each person. So, putting it all together: ( ρ water )(12 V log ) g = ( ρ log )(12 V log ) g + n ( mg ) Solve that for n : First, divide both sides by g : ( ρ water )(12 V log ) = ( ρ log )(12 V log ) + nm Subtract ( ρ log )(12 V log ) from each side: ( ρ water )(12 V log ) – ( ρ log )(12 V log ) nm Clean it up by factoring out 12 V log : 12
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This note was uploaded on 03/27/2010 for the course PH 202 taught by Professor Staff during the Spring '08 term at Oregon State.

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HW1-2Sol - Oregon State University Physics 202 HW1-2...

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