Bucket A and block C are connected by a cable that passes over drum B. Knowing that drum B rotates slowly counterclockwise and that the coefficients of friction at all surfaces are μS = 0.35 and μk = 0.25, determine the smallest combined mass m of the bucket and its content for which block C will (a) remain at rest, (b) start moving up the incline, (c) continue moving up the incline at a constant speed.
Fig. P8.118
(a)
Find the smallest combined mass m of the bucket for the block C will remain at rest.
Answer to Problem 8.118P
The smallest combined mass m of the bucket is
Explanation of Solution
Given information:
The mass of the block C is
The coefficient of static friction is
The coefficient of kinetic friction is
Calculation:
Show the free-body diagram of the drum B as in Figure 1.
Find the angle of the belt wounded around the drum as follows;
Find the tension
Substitute mg for
Here, the acceleration due to gravity is g.
Consider the value of acceleration due to gravity is
Show the free-body diagram of the block C as in Figure 2.
At rest, the cable slips on the drum. The motion impending is along the x-axis.
Substitute
Resolve the horizontal component of forces.
Substitute 100 kg for
Find the friction force (F) using the relation.
Substitute 0.35 for
Resolve the vertical component of forces.
Substitute
Therefore, the smallest combined mass m of the bucket is
(b)
Find the smallest combined mass m of the bucket for the block C start moving up the incline.
Answer to Problem 8.118P
The smallest combined mass m of the bucket is
Explanation of Solution
Given information:
The mass of the block C is
The coefficient of static friction is
The coefficient of kinetic friction is
Calculation:
Show the free-body diagram of the block C as in Figure 3.
When the block start moving up the incline;
No slipping occurs at block and drum. The motion impending is against the x-axis.
Substitute
Resolve the horizontal component of forces.
Substitute 100 kg for
Find the friction force (F) using the relation.
Substitute 0.35 for
Resolve the vertical component of forces.
Substitute
Therefore, the smallest combined mass m of the bucket is
(c)
Find the smallest combined mass m of the bucket for the block C continue moving up the incline at constant speed.
Answer to Problem 8.118P
The smallest combined mass m of the bucket is
Explanation of Solution
Given information:
The mass of the block C is
The coefficient of static friction is
The coefficient of kinetic friction is
Calculation:
Show the free-body diagram of the block C as in Figure 3.
When the block start moving up the incline;
No slipping occurs at block and drum. The motion impending is against the x-axis.
Substitute
Resolve the horizontal component of forces.
Substitute 100 kg for
Find the friction force (F) using the relation.
Substitute 0.25 for
Resolve the vertical component of forces.
Substitute
Therefore, the smallest combined mass m of the bucket is
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Chapter 8 Solutions
VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)
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