PHYSICS HIGH SCHOOL

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 3 inches in diameter can transmit 46 hp at 100 rpm, what must the diameter be in order to transmit 74 hp at 175 rpm?

Answers

Answer 1

Answer:

Answer:

diameter ≅ 3 inches

Explanation:

$HP=k*s*d^(3)$

Use a constant factor, k

Let Hp = horsepower

Let s = speed in rpm

Let d = diameter in inches

to find constant k, using

Hp=46

S=100

d=3 in

$46=k*100*3^(3) \n\n46=k*100*27\n46=2700k\nk=(46)/(2700) \nk=0.017\n\n$

To find diameter when;

Hp=74

S=175

k=0.017

d=d inches

$74=0.017*175*d^(3) \n\n74=2.975*d^3\nd^3=(74)/(2.975) \nd=\sqrt[3]{24.87} \nd=2.9 inches\n\n$ d≅ 3 inches

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