Concept explainers
The system shown starts from rest, and the length of the upper cord is adjusted so that A, B, and C are initially at the same level. Each component moves with a constant acceleration, and after 2 s the relative change in position of block C with respect to block A is 280 mm upward. Knowing that when the relative velocity of collar B with respect to block A is 80 mm/s downward, the displacements of A and B are 160 mm downward and 320 mm downward, respectively, determine (a) the accelerations of A and B if
(a)
The acceleration of ‘A’ and ‘B’ if
Answer to Problem 11.60P
Explanation of Solution
Given information:
At
Each component moves in constant acceleration
After
The relative change in position of block ‘C’ with respect to block ‘A’ is
The velocity of collar ‘B’ with respect to ‘A’ is
The displacement of block ‘A’ is
The displacement of collar ‘B is
In a dependent motion of particles such as the pulley system shown above,
The total length of the rope is a constant
For example,
Calculation:
In above system, the length of each cable is constant
For cable 1,
Differentiate above equation twice,
For cable 2,
Differentiate above equation twice,
For block ‘A’
For block ‘C’
Therefore,
At,
But we know that,
Then,
For block ‘A’
For block ‘B’
Then,
But we have already found,
Therefore,
Then, for block ‘A’
Then, for collar ‘B’
Conclusion:
The acceleration of ‘A’ and ‘B’ are
(b)
The change in position of block ‘D’ when the velocity of block ‘C’ is
Answer to Problem 11.60P
Explanation of Solution
Given information:
At
Each component moves in constant acceleration
After
The relative change in position of block ‘C’ with respect to block ‘A’ is
The velocity of collar ‘B’ with respect to ‘A’ is
The displacement of block ‘A’ is
The displacement of collar ‘B is
For a uniformly accelerated motion,
In above equation,
Calculation:
According to sub part a,
We have found
Bu we know that,
Therefore,
When,
Therefore,
To find the change in distance of block ‘D’
Conclusion:
The change in distance of block ‘D’ is equal to
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Chapter 11 Solutions
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