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Question 1137749: Can someone please help?
Use the given information to answer the question.
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 4 inches in diameter can transmit 40 hp at 120 rpm, what must the diameter, d, be in order to transmit 65 hp at 140 rpm? (Round your answer to two decimal places.)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let d be the diameter, then
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hp = k * rpm * d^3, where k is the constant of proportionality
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We are given that
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40 = k * 120 * 4^3
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k = 40/(120 * 64) = 1/192
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65 = (1/192) * 140 * d^3
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multiply both sides of = by 192
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12480 = 140 * d^3
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d^3 = 12480/140 = 89.1429
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d = 89.1429^(1/3) = 4.4671
:
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The diameter is 4.47 inches
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