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- Homework Statement
- This was posed as a challenge problem by Professor Richard Wolfson as part of a physics course he recorded for TGC company. Problem: A flatboat has dimensions 3m long, 1 m wide and .24 m deep and has mass of 120 kg and is on a lake (fresh water). What is the upward force on the boat and how many 85 kg people can get on the boat before it is swamped?

- Relevant Equations
- density = mass/volume; density of water is 1000 kg/m(3)

Apply Principle of Archimedes - upward force is equal to the weight of the volume of water displaced. Density (boat) = 120 kg/(3x1x.24)m(3) = 500/3 kg/m(3)

Density of water = 1000kg/m(3). Density (water)/Density of boat = 1000 kg/m(3)/(500/3) kg/m(3) = 6. So density of water is 6 times the density of the boat and so boat obviously floats. Now I reasoned that if the density of the boat with X people aboard floats it will just equal the density of water.

(1) Let X = number of 85-kg people. We have (120 + X 85)/(3x1x.24) = (120 +85X)/.72 = 1000 -> X = 7.1 people. Since we can't have a .1 person, the boat can hold 6 people, each with mass 85 kg. That checks with the answer given (boat can hold 6 people), but not sure logic is correct. Finding the upward force has got me stumped. The answer is 590 N. When I substitute 6-85 kg people into the boat into Equation (1) above, I only get about 520 N. (Note: Professor Wolfson used g = 10 m/sec (2) to simplify the math.) Any comments welcome!

Density of water = 1000kg/m(3). Density (water)/Density of boat = 1000 kg/m(3)/(500/3) kg/m(3) = 6. So density of water is 6 times the density of the boat and so boat obviously floats. Now I reasoned that if the density of the boat with X people aboard floats it will just equal the density of water.

(1) Let X = number of 85-kg people. We have (120 + X 85)/(3x1x.24) = (120 +85X)/.72 = 1000 -> X = 7.1 people. Since we can't have a .1 person, the boat can hold 6 people, each with mass 85 kg. That checks with the answer given (boat can hold 6 people), but not sure logic is correct. Finding the upward force has got me stumped. The answer is 590 N. When I substitute 6-85 kg people into the boat into Equation (1) above, I only get about 520 N. (Note: Professor Wolfson used g = 10 m/sec (2) to simplify the math.) Any comments welcome!