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73. Problem 17.43 (RHK) Three children each of weight 82.4 lb make a log raft by lashing together logs of diameter 1.05 ft and length 5.80 ft. How many logs will be needed to keep them afloat? We can take the density of the wood to be 47.3 lb/ft3. |
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Solution: Click For PDF Version Volume, v, of each log will be
Weight of each log, w, is
Let the number of logs required for keeping three children each of weight 82.4 lb be n. The total weight of the logs and that of the children will be
Density of water in lb/ft3 is 62.43 lb/ft3. Buoyant force in water for keeping the logs and the children afloat will be volume of the logs times the density of water in lb/ft3. We, therefore, have the equation from which n can be solved.
We find
Therefore, 4 logs will be needed for making a raft that will keep the three children afloat.
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where d is the diameter and l is the length of each log.
Therefore,
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