Explanation Given information: Weight of hemisphere is=W Radius of hemisphere is=r Consider the free body diagram. Equation for acceleration about the point O is, a O = a A + a O / A a O = a A + r α Substituting all the required values we will get, a O = a A + r α a O = 0 + r α = r α Acceleration about centroid is, a ¯ = a G a ¯ = a O + a α G / O a ¯ = ( r α ) + ( x ¯ α ) Then the acceleration component along x and y is, a ¯ = ( r α ) + ( x ¯ α ) The acceleration in x-direction a x = r α . Acceleration in y direction is a y = x ¯ α . Take the moment about point A. ∑ 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 α ( m r 2 + m x 2 ¯ + m k 2 ) = m g x ¯ α = m g x ¯ ( m r 2 + m x 2 ¯ + m k 2 ) α = g x ¯ ( r 2 + x 2 ¯ + k 2 ) − − − ( 1 ) Then the equation of motion in that the external force is equivalent to the effective forces. ∑ F x = ∑ ( F x ) e f f F = m a x Substituting all required values we get, F = m a x = m r α Equate the forces in y direction To determine (b) The acceleration of point B.

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Chapter 16.2, Problem 16.111P

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 16.110P

Chapter 16.2, Problem 16.112P

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(a) The minimum value of coefficient of friction.

Solution Summary: The author explains the minimum value of coefficient of friction in the free body diagram.