Cylinder A is moving downward with a velocity of 3 m/s when the brake is suddenly applied to the drum. Knowing that the cylinder moves 6 m d

Question

Cylinder A is moving downward with a velocity of 3 m/s when the brake is suddenly applied to the drum. Knowing that the cylinder moves 6 m downward before coming to rest and assuming uniformly accelerated motion, determine (a) the angular acceleration of the drum, (b) the time required for the cylinder to come to rest.

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Maris 4 years 2021-08-17T14:44:31+00:00 1 Answers 32 views 0

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  1. Jezebel
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    2021-08-17T14:45:33+00:00
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    Answer:

    Incomplete question

    Check attachment for the given diagram

    Explanation:

    Given that,

    Initial Velocity of drum

    u=3m/s

    Distance travelled before coming to rest is 6m

    Since it comes to rest, then, the final velocity is 0m/s

    v=3m/s

    Using equation of motion to calculate the linear acceleration or tangential acceleration

    v²=u²+2as

    0²=3²+2×a×6

    0=9+12a

    12a=-9

    Then, a=-9/12

    a=-0.75m/s²

    The negative sign shows that the cylinder is decelerating.

    Then, a=0.75m/s²

    So, using the relationship between linear acceleration and angular acceleration.

    a=αr

    Where

    a is linear acceleration

    α is angular acceleration

    And r is radius

    α=a/r

    From the diagram r=250mm=0.25m

    Then,

    α=0.75/0.25

    α =3rad/sec²

    The angular acceleration is =3rad/s²

    b. Time take to come to rest

    Using equation of motion

    v=u+at

    0=3-0.75t

    0.75t=3

    Then, t=3/0.75

    t=4 secs

    The time take to come to rest is 4s

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