Concept explainers
(a)
The accelerations of A
(a)
Answer to Problem 11.60P
The accelerations of A
Explanation of Solution
Given information:
The relative change in position of block C with respect to block A
The relative velocity of collar B with respect to block A
The displacement of A
The displacement of B
Calculation:
Show the length and position of the cables as in Figure (1).
Choose the coordinate downward positive and right side positive.
Write the express for total lengths of cables 1:
Differentiate the above equation with respective to time (t).
Denotes
Differentiate the equation (2) with respective to time (t).
Denotes
Write the express for total lengths of cables 2:
Differentiate the above equation with respective to time (t).
Denotes
Differentiate the equation (3) with respective to time (t).
Denotes
At time (t) 0 sec the velocity (v) is zero.
Then, the initial position of cable A, cable B and cable C is equal.
Calculate the position
Here,
Substitute 0 for
Calculate the position
Here,
Substitute 0 for
Calculate the position
Here,
Substitute 0 for
Write the expression for relative change in position of block C with respect to block A:
Substitute
Write the equation for acceleration
Substitute
Calculate the acceleration of block A:
Substitute
Calculate the velocity
Substitute 0 for
Calculate the velocity
Substitute 0 for
Write the equation for relative velocity of block B with respect to block A
Substitute
Substitute
Modify the equation (5).
Substitute
Modify the equation (7).
Substitute
Calculate the time (t):
Substrate equation (13) and (12).
Substitute
Calculate the acceleration
Substitute 4 sec for t in equation (12).
Therefore, the accelerations of A
(b)
The change in position
(b)
Answer to Problem 11.60P
The change in position
Explanation of Solution
Given information:
The relative change in position of block C with respect to block A
The relative velocity of collar B with respect to block A
The displacement of A
The displacement of B
The velocity
Calculation:
Calculate the acceleration
Substitute
Calculate the acceleration
Substitute
Calculate the time (t) using the relation below;
Here,
Substitute 0 for
Calculate the change in positon
Here,
Substitute 0 for
Therefore, the change in position
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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