Explanation Given information: Weight of hemisphere is = W Radius of hemisphere is = r Consider the free body diagram. Formula for acceleration of point O. a O = a A + a O / A − − − ( 1 ) Find the relative acceleration between point O and A. a O / A = r α Substituting the values we get, a O = 0 + r α = r α Formula for acceleration of point G as, a G = a O + a G / O − − − − ( 2 ) Find the relative acceleration between point O and G. a G / O = x α Substituting all the required values we get, a G = r α + x α Formula for acceleration of the system is, a = a G a = r α + x α − − − ( 3 ) Then, the horizontal component of acceleration a x . a x = r α The vertical component of acceleration a y . a y = x α Free body diagram of the given system Free body diagram for kinetic system is, Take the moment about point A. Here, the external force is equivalent to system of effective forces. Formula for the system of external moment as, ∑ M A = ∑ ( M A ) e f f − − − ( 4 ) Find the value of ∑ M A . ∑ M A = W x Find the value of ∑ ( M A ) e f f . ∑ ( M A ) e f f = ( m a x ) r + ( m a y ) x + I α Find the moment of inertia of the system. I = m k 2 Find the weight of the system. W=mg From the equation (4) we know that, ∑ M A = ∑ ( M A ) e f f W x = ( m a x ) r + ( m a y ) x + I α m g x = ( m ( r α ) ) r + ( m ( x α ) ) x + m k 2 α g x = ( r 2 + x 2 + k 2 ) α α = g x ( r 2 + x 2 + k 2 ) − − − ( 5 ) External forces is equivalent to the system of effective forces. ∑ F x = ∑ ( F x ) e f f − − − ( 6 ) Find the ∑ F x value. ∑ F x = F Find the ∑ ( F x ) e f f value. ∑ ( F x ) e f f = m a x ∑ F x = ∑ ( F x ) e f f F = m a x = m r α Similarly, ∑ F y = ∑ ( F y ) e f f − − − ( 7 ) Here, the upward force is positive To determine (b) The acceleration of point B.

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 16.2, Problem 16.112P

To determine

(a)

The minimum value of coefficient of friction.

To determine

(b)

The acceleration of point B.

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Chapter 16.2, Problem 16.111P

Chapter 16.2, Problem 16.113P

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(a) The minimum value of coefficient of friction.

Solution Summary: The author explains that the minimum value of coefficient of friction is mu _mathrmmin=.