SOLUTION: The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute rpm) and the cube of its diameter. If the shaft of a certain material

Algebra ->  Equations -> SOLUTION: The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute rpm) and the cube of its diameter. If the shaft of a certain material       Log On


   

Question 1141267: The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute rpm) and the cube of its diameter. If the shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 73 hp at 45 rpm?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use a constant factor, +k+
Let +H+ = horsepower
Let +s+ = speed in rpm
Let +d+ = diameter in inches
+H+=+k%2As%2Ad%5E3+
+36+=+k%2A75%2A2%5E3+
+36+=+600k+
+k+=+.06+
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+73+=+.06%2A45%2Ad%5E3+
+73+=+2.7%2Ad%5E3+
+d%5E3+=+27.037+
+d+=+3.00136+ in
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check the math & get a 2nd opinion if needed