phys124s11-hw03

phys124s11-hw03 - HW 7 Solutions Buoyant Ping-Pong Ball A...

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1 HW 7 Solutions Buoyant Ping-Pong Ball A Ping-Pong ball is held submerged in a bucket of water by a string attached to the bucket's bottom. a) Salt is now added to the water in the bucket, increasing the density of the liquid. What happens to the tension in the string? The tension in the string balances the sum of the object's weight and the buoyant force. Tension Buoyancy Force Weight =− . By adding salt, we increase the mass density of water, and, hence, the buoyancy force. The tension does not change. The tension increases. The tension decreases. b) What happens to the tension in the string if the Ping-Pong ball is replaced by a smaller spherical object of equal weight? The tension does not change. The tension increases. The tension decreases. Since the Ping-Pong ball is replaced by an object of equal weight, the weight remains the same, but the buoyant force on the object is decreased in comparison to the buoyant force experienced by the Ping-Pong ball. Test Your Understanding 14.2: Pressure in a Fluid Two identical vertical tubes, each 1.00 cm in diameter and 50.0 cm tall, are each filled with a liquid. The liquid in tube #1 has density 1500 kg/m 3 , whereas the liquid in tube #2 has density 2000 kg/m 3 . The top of each tube is exposed to the air. The pressure in the air above the two tubes is now increased from 1.00 atm to 2.00 atm. In which tube does this cause the greatest pressure increase at the bottom of the tube? Pascal's law states that an additional pressure applied at one point in a fluid is transmitted undiminished to all other points in the fluid. In this situation an additional pressure of 1.00 atm is applied to the top of each fluid-filled tube, so this causes an additional pressure of 1.00 atm at the bottom of each tube. If now a pressure of 2.00 atm is applied to the top of each fluid-filled tube, this would cause an additional pressure of 1.00 atm at the bottom of each tube. Thus, the pressure increase is the same in both tubes. Test Your Understanding 14.3: Buoyancy
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2 For which of the following pairs of objects is the buoyant force the same for both members of the pair? a 1.00-cm 3 cube of iron and a 1.00- cm 3 cube of aluminum, both submerged in water a 1.00-kg cube of iron and a 1.00-kg cube of aluminum, both submerged in water both of the above none of the above From Archimedes's principle, the buoyant force on a submerged object equals the weight of the displaced fluid. If two objects have the same volume, they both displace the same volume of fluid and hence the same weight of fluid and so are subject to the same buoyant force. Test Your Understanding 14.4: Fluid Flow An ideal incompressible fluid flows through a horizontal tube of radius 2.00 cm. At one point along the tube's length there is a constriction where the radius is only 1.00 cm. Compared to the volume flow rate in the 2.00-cm-radius portion of the tube, the volume flow rate in the 1.00-cm- radius portion of the tube is 4 times as great the same 2 times as great as great as great not enough information is given to decide
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phys124s11-hw03 - HW 7 Solutions Buoyant Ping-Pong Ball A...

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