
(a)
The acceleration of two blocks after they released from rest.
(a)

Answer to Problem 127P
Acceleration of block 1 is
Acceleration of block 2 is
Explanation of Solution
Mass of block
The free body diagram is shown below.
Write the equation for net force on block 1 in vertical direction.
Here, the normal reaction force on block 1 is
Write the equation for net force on block 1 in horizontal direction.
Here, the tension on string is
Write the equation for net force on block 2 in vertical direction.
Here, the mass of block 2 is
Write the condition to avoid the shrinking of cords.
Here, the acceleration in right direction is taken as positive and in downward direction is taken as negative quantity.
Introduce a new common variable in place of
Here, the new variable to denote the acceleration is
Rewrite equations
Rewrite equations (II) and (III) in terms of
Equate the right hand sides of above two equations.
Conclusion:
Substitute
The direction of acceleration of each block is same as that of the tension on string connecting the pulley and each block. Tension on string connecting
Therefore, the acceleration of block 1 is
(b)
The velocity of
(b)

Answer to Problem 127P
The velocity is
Explanation of Solution
Mass of block
Write the Newton’s equation to find the velocity of
Here, the velocity of
Conclusion:
Substitute
Due to tension on string,
Therefore, the velocity is
(c)
The displacement of
(c)

Answer to Problem 127P
Displacement is
Explanation of Solution
Mass of block
Write the Newton’s equation to find the displacement of
Here, the displacement of
Conclusion:
Substitute
Therefore, the displacement is
(d)
The displacement of
(d)

Answer to Problem 127P
The displacement of
The displacement of
Explanation of Solution
Mass of block
Conclusion:
Substitute
Substitute
Therefore, the displacement of
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