Aqua running is a form of cardiovascular conditioning in which a person runs while partially submerged in water. If an aqua runner (mass 80 kg, weight 784 N) is exactly 50% submerged in water, what is the apparent weight of the runner? (Note: Assume the density of both the water and the runner is 1.0 g/cm3.)A.157 NB.196 NC.261 ND.392 N
Question
Aqua running is a form of cardiovascular conditioning in which a person runs while partially submerged in water. If an aqua runner (mass 80 kg, weight 784 N) is exactly 50% submerged in water, what is the apparent weight of the runner? (Note: Assume the density of both the water and the runner is 1.0 g/cm3.)A.157 NB.196 NC.261 ND.392 N
Solution
The apparent weight of an object in a fluid is given by the actual weight of the object minus the buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object.
Given that the runner is exactly 50% submerged in water, this means that the runner has displaced an amount of water equal to 50% of their own volume.
Since the density of the runner and the water are the same (1.0 g/cm3), this means that the weight of the water displaced is equal to 50% of the weight of the runner.
So, the buoyant force is 50% of 784 N, which is 392 N.
The apparent weight of the runner is then the actual weight minus the buoyant force, which is 784 N - 392 N = 392 N.
So, the answer is D. 392 N.
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