The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear veloci

Question

The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 14 miles per hour, how fast would the pulley need to turn (in revolutions per minute)

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Doris 5 years 2021-07-14T14:09:55+00:00 1 Answers 30 views 0

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  1. Nem
    0
    2021-07-14T14:11:04+00:00
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    Answer:

    13.94 rpm

    Explanation:

    Given that,

    The diameter of the pulley, d = 14 foot

    Radius, r = 7 foot

    The linear velocity of the pulley, v = 14 mph = 20.53 ft/s

    We need to find the angular velocity in rpm.

    We know that, the relation between the linear velocity and the angular velocity is as follows :

    v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{20.53}{14}\\\\\omega=1.46\ rad/s

    or

    \omega=13.94\ rpm

    So, the angular velocity of the pulley is 13.94 rpm.

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