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Unformatted text preview: Physics 101 Classical Physics Spring 2010 Homework 9 Solutions DUE IN CLASS ON April 8 1. A certain object floats in fluids of density: 1. 0.9 ; 2. ; 3. 1.1 . Rank these fluids according to the magnitude of the buoyant force they exert on the object, least to greatest. (a) 1,2,3 (b) 3,2,1 (c) 2,3,1 (d) 3,1,2 (e) All are the same . Since the object is floating, it is at rest in the vertical direction. Therefore, the sum of the forces in the vertical direction must be zero. There is gravity acting downwards on the object, and the only force acting upwards is the buoyant force. So, the buoyant force must be equal in magnitude to the force due to gravity which depends only on the object not the fluid it is in. Therefore, the buoyant force is the same in each of the three fluids. 2. A pirate chest rests flat and is half-buried in the bottom of an ocean. If the water is still, the net force it exerts on the chest: (a) is downward , (b) is upward, (c) depends on the mass of the chest, (d) is zero, (e) depends on the contents of the chest The chest will have a force due to the pressure of the fluid acting at all points on the half of the chest that is exposed. Along each side of the chest the force on that side will be canceled by the force on the opposite side, so the net force on the sides is zero. This leaves the top of the chest, which means the net force the water exerts on the chest is downwards. 3. In a stationary homogeneous liquid: (a) pressure is the same at all points, (b) pressure depends on direction, (c) pressure is independent of any atmospheric pressure on the upper surface of the liquid, (d) pressure is the same at all points at the same level , (e) none of the above Each point at a given level has the same amount of fluid above it which is being acted on by gravity producing a uniform pressure at all points at equal levels. 1 4. A non-viscous incompressible liquid is flowing through a horizontal pipe of con- stant cross-section. Bernoullis equation and the equation of continuity predict that the drop in pressure along the pipe: (a) depends on the cross-sectional area of the pipe (b) depends on the height of the pipe (c) depends on the length of the pipe (d) is zero (e) depends on the fluid velocity Bernoullis principle and the equation of continuity imply that for a fluid in a horizontal pipe P + 1 2 v 2 = constant where P is the pressure of the fluid, is the density of the fluid, and v is the speed of the fluid flowing through the pipe. Since the cross-sectional area of the pipe is constant, the pressure must be constant, so the drop in pressure allong the pipe is zero. 5. A person blows across the top of one arm of a U-tube partially filled with water....
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