40. The ice with the bear on it is floating, so that the upward-acting buoyant REASONING force balances the downward-acting weight of the ice and weight of the bear. The Wice Wbear magnitude of the buoyant force is the weight of the displaced water, according to FB Archimedes’ principle. Thus, we have , the expression with which we will obtain We Wbear. can express each of the weights and as mass times the magnitude of the acceleration Wice due to gravity (Equation 4.5) and then relate the mass to the density and the displaced volume by using Equation 11.1. Since the ice with the bear on it is floating, the upward-acting buoyant force SOLUTION balances the downward-acting weight of the ice and the weight of the bear. FB Wice Wbear The buoyant force has a magnitude that equals the weight of the displaced water, as stated by Archimedes’ principle. Thus, we have (1) In Equation (1), we can use Equation 4.5 to express the weights and as mass times Wice m the magnitude of the acceleration due to gravity. Then, the each mass can be expressed as g (Equation 11.1). With these substitutions, Equation (1) becomes (2) When the heaviest possible bear is on the ice, the ice is just below the water surface and displaces a volume of water that is . Substituting this result into Equation (2), we find that 41. The buoyant exerted on the balloon by the air must be equal in REASONING magnitude to the weight of the balloon and its contents (load and hydrogen). The magnitude of the buoyant force is given by . Therefore, since the balloon is spherical, . Making this substitution for and solving for we V r, obtain Direct substitution of the data given in the problem yields SOLUTION 43. Since the duck is in equilibrium, its downward-acting weight is balanced by REASONING the upward-acting buoyant force. According to Archimedes’ principle, the magnitude of the buoyant force is equal to the weight of the water displaced by the duck. Setting the weight of the duck equal to the magnitude of the buoyant force will allow us to find the average density of the duck.
40. REASONING The ice with the bear on it is floating, so that the upward-acting buoyant force balances the downward-acting weight Wice of the ice and weight Wbear of the bear. The magnitude FB of the buoyant force is the weight of the displaced water, according to Archimedes’ principle. Thus, we have , the expression with which we will obtain Wbear. We can express each of the weights and Wice as mass times the magnitude of the acceleration due to gravity (Equation 4.5) and then relate the mass to the density and the displaced volume by using Equation 11.1. SOLUTION Since the ice with the bear on it is floating, the upward-acting buoyant force FB balances the downward-acting weight Wice of the ice and the weight Wbear of the bear. The buoyant force has a magnitude that equals the weight of the displaced water, as stated by Archimedes’ principle. Thus, we have (1) In Equation (1), we can use Equation 4.5 to express the weights and Wice as mass m times the magnitude g of the acceleration due to gravity. Then, the each mass can be expressed as (Equation 11.1). With these substitutions, Equation (1) becomes (2) When the heaviest possible bear is on the ice, the ice is just below the water surface and displaces a volume of water that is . Substituting this result into Equation (2), we find that 41. REASONING The buoyant exerted on the balloon by the air must be equal in magnitude to the weight of the balloon and its contents (load and hydrogen). The magnitude of the buoyant force is given by . Therefore, since the balloon is spherical, . Making this substitution for V and solving for r, we obtain SOLUTION Direct substitution of the data given in the problem yields 43. REASONING Since the duck is in equilibrium, its downward-acting weight is balanced by the upward-acting buoyant force. According to Archimedes’ principle, the magnitude of the buoyant force is equal to the weight of the water displaced by the duck. Setting the weight of the duck equal to the magnitude of the buoyant force will allow us to find the average density of the duck.
ch_11_hw_40-41-43-61-62.docx