
8.134 and 8.135 The coefficients of friction are μS = 0.40 and μk = 0.30 between all surfaces of contact. Determine the smallest force P required to start the 30-kg block moving if cable AB (a) is attached as shown, (b) is removed.
(a)

Find the smallest value of P required to start moving the 30 kg block if the cable AB is attached.
Answer to Problem 8.134RP
The smallest force P required to move the 30-kg block is
Explanation of Solution
Given information:
The coefficient of static friction is
The coefficient of kinetic friction is
Calculation:
Consider the acceleration due to gravity as
Find the weight of the 20-kg mass block as follows;
Find the weight of the 30-kg mass block as follows;
Show the free-body diagram of the 20-kg mass block as in Figure 1.
Find the normal force
Find the friction force
Substitute 0.40 for
Find the tension in the cable AB (T) by resolving the horizontal component of forces.
Show the free-body diagram of the 30-kg mass block as in Figure 2.
Find the normal force
Find the friction force
Substitute 0.40 for
Find the force P by resolving the horizontal component of forces.
Therefore, the smallest force P required to move the 30-kg block is
(b)

Find the smallest value of P required to start moving the 30 kg block if the cable is removed.
Answer to Problem 8.134RP
The smallest force P required to move the 30-kg block is
Explanation of Solution
Given information:
The coefficient of static friction is
The coefficient of kinetic friction is
Calculation:
Consider the acceleration due to gravity as
Find the weight of the 20-kg mass block as follows;
Find the weight of the 30-kg mass block as follows;
Show the free-body diagram of the block assembly as in Figure 3.
Find the normal force (N) by resolving the vertical component of forces.
Find the friction force (F) using the relation.
Substitute 0.40 for
Find the force P by resolving the horizontal component of forces.
Therefore, the smallest force P required to move the 30-kg block is
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Chapter 8 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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