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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?

Respuesta :

Kazeemsodikisola

Answer:

Explanation:

Given that

Tangential acceleration (at) =3m/sĀ²

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

And also the change in time āˆ†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=vĀ²/r

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

v=u+at

Where (a) is the tangential acceleration = 3m/sĀ²

And the is final time at t=5sec

v=0+3Ɨ5

v=0+15

v=15m/s

Then, ac=vĀ²/r

ac=15Ā²/1.5

ac=150m/sĀ²

Then, the total acceleration is given as

a=āˆš(at)Ā²+(ac)Ā²

Since at=3m/sĀ² and ac=150m/sĀ²

Then,

a=āˆš3Ā²+150Ā²

a=āˆš22509

a=150.03m/sĀ²

The total acceleration is 150.03m/sĀ²

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