algebra

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The horsepower (hp) that a shaft can safety transmit varies jointly with its speed (in revolutions per minute, or rpm) and the cube of the diameter. If a shaft of a certain material 2 in in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 150 hp at 20 rpm?

  • algebra -

    just plug and chug:

    hp = k*s*d^3

    36 = k * 75 * 2^3

    k = 36/(75 * 8) = 36/600

    now, for the unknown d

    150 = k * 20 * d^3
    150 = 36/600 * 20 * d^3

    150 * 600/36 * 1/20 = d^3

    125 = d^3

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