Ask Question
19 February, 14:36

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?

+2
Answers (1)
  1. 19 February, 15:21
    0
    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
Know the Answer?