
Concept explainers
(a)
Find the acceleration of block A for each system.
(a)

Answer to Problem 12.15P
The acceleration of block A for system 1 is
The acceleration of block A for system 2 is
The acceleration of block A for system 1 is
Explanation of Solution
Calculation:
Sketch the general diagram of systems as shown in Figure (1).
Write total length of cable connecting block A and block B.
Here,
Differentiate Equation (1) with respect to t to write velocity of the blocks.
Here,
Differentiate Equation (2) with respect to t to write acceleration of the blocks.
First of all check the required static friction with static friction to maintain equilibrium.
Sketch the free body diagram and kinetic diagram of block A as shown in Figure (2).
Refer Figure (2).
Consider downward direction as positive.
Apply Newton’s law of motion along y-axis.
Here, T is the tension in the cable,
Sketch the free body diagram and kinetic diagram of block B as shown in Figure (3).
Refer Figure (3).
Consider downward direction as positive.
Apply Newton’s law of motion along y-axis.
Find the equation of acceleration of block A.
Here, T is the tension in the cable,
Substitute
The initial velocity of block A is zero.
Find the equation of velocity of block A using kinematics:
Here,
Substitute At
Find the equation of time required for block A to reach any velocity.
Find the acceleration of block A
Substitute 200 lb for
Therefore, the acceleration of block A for system 1 is
Find the acceleration of block A
Substitute 200 lb for
Therefore, the acceleration of block A for system 2 is
Find the acceleration of block A
Substitute 2200 lb for
Therefore, the acceleration of block A for system 2 is
(b)
Find the velocity of block A for each system after it has moved through 10 ft
(b)

Answer to Problem 12.15P
The velocity of block A for system 1 after it has moved through 10 ft is
The velocity of block A for system 2 after it has moved through 10 ft is
The velocity of block A for system 3 after it has moved through 10 ft is
Explanation of Solution
Calculation:
Find the velocity of block A for system 1
Substitute
Thus, the velocity of block A for system 1 after it has moved through 10 ft is
Find the velocity of block A for system 2
Substitute
Thus, the velocity of block A for system 2 after it has moved through 10 ft is
Find the velocity of block A for system 3
Substitute
Thus, the velocity of block A for system 3 after it has moved through 10 ft is
(c)
Find the time required for block A to reach a velocity of 20 ft/s
(c)

Answer to Problem 12.15P
The time required for block A for system 1 to reach a velocity of 20 ft/s is
The time required for block A for system 2 to reach a velocity of 20 ft/s is
The time required for block A for system 3 to reach a velocity of 20 ft/s is
Explanation of Solution
Calculation:
Find the time required for block A for system 1
Substitute
Thus, the time of required for block A for system 1 to reach a velocity of 20 ft/s is
Find the time required for block A for system 2
Substitute
Thus, the time of required for block A for system 2 to reach a velocity of 20 ft/s is
Find the time required for block A for system 3
Substitute
Thus, the time of required for block A for system 3 to reach a velocity of 20 ft/s is
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Chapter 12 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
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