A large cylindar of radius 1.55 m is rotating about an axis through its center a

Question

A large cylindar 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 cylindar at a constant height above the bottom. A) What is the minimum angular speed in rev/min for the block to not slide down the wall? B) What is the magnitude of the normal force the wall exerts on the block? C) If the coefficient of static frictin increases, What happens to the minimum angular speed? Explain?

2. (30 pts). 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 cylinder 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 revlmin for the block to not slide down the wall? B) What is the magnitude of the normal force the wall exerts on the block? c) lf the coefficient of static friction increases, what happens to the minimum angular speed? Explain? Pictorial Representation

Explanation / Answer

A) Let the minimum angular speed be w

um(w*2 pi/60)^2 r = mg

w^2 * 0.011*1.55 = 9.8/0.456

w = sqrt(9.8/(0.011*1.55*0.456))

= 35.5 rev/min

B) N = mW^2 r

   = 1.25*(35.5*2pi/60)^2 *1.55

   = 26.77 N answer

C) if coefficient of static friction increases, minimum angular speed decreases. It is obvious from the first equation in part one.

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