
(a)
The maximum velocity of each block if the coefficient of kinetic friction between block and the surface is 0.
(a)

Answer to Problem 59P
The maximum velocity of each block is
Explanation of Solution
Given info: The force constant is
Write the expression to calculate the force by the spring.
Here,
Substitute
Write the expression of conservation of energy.
Here,
Substitute
Write the expression of conservation of linear momentum.
Substitute
Substitute
Substitute
Thus, the maximum velocity of each block is
Conclusion:
Therefore, the maximum velocity of each block is
(b)
The maximum velocity of each block if the coefficient of kinetic friction between block and the surface is
(b)

Answer to Problem 59P
The maximum velocity of each block is
Explanation of Solution
Given info: The force constant is
Write the expression to calculate the normal force on the lighter block.
Here,
Substitute
Write the expression to calculate the limiting frictional force.
Here,
Substitute
The spring force,
Since the mass of right block is double than the left block therefore the limiting
The limiting frictional force of right clock is greater than the spring force so it will not move.
The left will continue to move as long as the spring force is large than the friction force.
Write the expression to calculate the limiting frictional force.
Here,
Substitute
Write the expression of conservation of energy.
Substitute
The negative sign indicates that the direction of motion of the lighter block is toward negative x axis.
The velocity of the heavier block is zero.
Thus, the maximum velocity of each block is
Conclusion:
Therefore, the maximum velocity of each block is
(c)
The maximum velocity of each block if the coefficient of kinetic friction between block and the surface is
(c)

Answer to Problem 59P
The velocity of both blocks is 0.
Explanation of Solution
Given info: The force constant is
Write the expression to calculate the limiting frictional force of left block.
Substitute
Write the expression to calculate the limiting frictional force of right block.
Substitute
The spring force is less than the limiting frictional force of both the blocks so the blocks will not move.
Conclusion:
Therefore, the velocity of both blocks is 0.
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Chapter 8 Solutions
Principles of Physics: A Calculus-Based Text
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