2 (30pts) A large cylinder of radius 1.55 m is rotating about an axis through it

Question

2 (30pts) A large cylinder of radius 1.55 m is rotating about an axis through its center as shown. A block of mass 1.25 kg rotates with the cyinder at a constant height above the bottom. The coefficients of static and kinetic friction between the block and the cylinder wall are 0 456 and 0.235. A) What is the minimum angular speed in rev/min for the block to not slide down the wal? B) What is the magnitude cof the normal force the wall exerts on the block? C) If the coefficient of static friction increases, what happens to the minimum angular speed? Explain? Pictorial Representation

Explanation / Answer

(A) in horizontal, N = m a_c = m w^2 r

and fmax= us N =us m w^2 r

in vertical, f - m g = 0

us m w^2 r = m g

0.456 w^2 = 9.8 / 1.55

w = 3.74 rad/s .........Ans

(B) N = m w^2 r = 27.1 N

(C) if us increases then w decreases.

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