A propeller blade at rest starts to rotate from t = 0 s to t = 5.0 s with a tangential acceleration of the tip of the blade at 3.00 m/s2. Th

Question

A propeller blade at rest starts to rotate from t = 0 s to t = 5.0 s with a tangential acceleration of the tip of the blade at 3.00 m/s2. The tip of the blade is 1.5 m from the axis of rotation. At t = 5.0 s, what is the total acceleration of the tip of the blade?

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Lệ Thu 2 months 2021-09-02T14:51:25+00:00 1 Answers 0 views 0

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    2021-09-02T14:53:06+00:00

    Answer:

    Explanation:

    Given that

    Tangential acceleration (at) =3m/s²

    The propeller blade starts from rest i.e. wo=0rad/sec

    And also the change in time ∆t=5sec

    Also radius of blade (r)=1.5m

    We have the tangential acceleration, so we need the centripetal acceleration

    Which is given as

    ac=v²/r

    Then we need to get the final velocity using equation of motion

    v=u+at

    Where (a) is the tangential acceleration = 3m/s²

    And the is final time at t=5sec

    v=0+3×5

    v=0+15

    v=15m/s

    Then, ac=v²/r

    ac=15²/1.5

    ac=150m/s²

    Then, the total acceleration is given as

    a=√(at)²+(ac)²

    Since at=3m/s² and ac=150m/s²

    Then,

    a=√3²+150²

    a=√22509

    a=150.03m/s²

    The total acceleration is 150.03m/s²

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