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A metal block of mass 265 g rests at a point 2.4 m from the center of a horizontal rotating wooden platform. The coefficient of static friction between the block and the platform is 0.257. The platform initially rotates very slowly but the rotation rate is gradually increasing. The acceleration of gravity is 9.8 m/s 2 . At what minimum angular velocity of the platform would the block slide away? Answer in units of rad/s.

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gilcarusolautaro

Answer:

The minimum angular velocity of the platform what whould the block slides away is w= 2.26 rad/s.

Explanation:

m= 0.265 kg

r= 2.4 m

μ= 0.257

g= 9.8 m/s²

W= m * g

W= 2.597 N

Fr= μ * W

Fr= 0.66 N

∑F = m * ac

W+Fr = m * ac

(W+ Fr) / m = ac

ac= 12.29 m/s²

ac= w² * r

√(ac/r)= w

w= 2.26 rad/s

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