A series of small packages, each with a mass of .5kg, are discharged from a conv

Question

A series of small packages, each with a mass of .5kg, are discharged from a conveyor belt as shown. Knowing that the coefficient of static friction between each package and the conveyor belt is 0.4, determine (a)the force exerted by the belt on the package just after it has passed point A, (b) the angle defining the point B where the packages first slip relative to the belt.

radius is 250mm. this question has been answered already however part B was incorrect. the answer for part B according to the book is 13.09 degrees. part a is 2.91N.

Explanation / Answer

a) Centrifugal force = mv^2/r = 0.5*1^2/0.25 = 2 N

Weight = mg = 0.5*9.81 = 4.91 N

net Normal force at A = 4.9 - 2 = 2.91 N

b) At B, component of weight normal to the belt = mg*Cos = 4.91*Cos

At B, net normal force = [4.91*Cos - 2] N (we have deducted centrifugal force.)

At B, Friction force = *normal force = 0.4*[4.91*Cos - 2] N

At B, Component of weigth tangential to belt = mgSin = 4.91*Sin

Packet will leave belt if friction force < 4.91*Sin

or, 0.4*[4.91*Cos - 2] < 4.91*Sin

Solving this graphically or iteratively, we get > 13.09 deg

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