Concept explainers
(a)
The maximum compression of the spring.
(a)
Answer to Problem 118P
The maximum compression distance of the spring is
Explanation of Solution
The figure 1 shows the forces acting on the block.
Write the equation for mechanical energy of the system
Here,
Write the equation for Newton’s second law of motion of the block with perpendicular to the plane in y direction.
Here,
Rewrite the equation (II) for normal force.
Write the equation for the frictional force.
Here,
Substitute equation (III) in equation (IV).
Replace
Here,
Substitute equation (V) in equation (VI).
Conclusion:
Solve the equation (VII) for
Substitute
Therefore, the maximum compression distance of the spring is
(b)
The distance of the block inclined before coming to rest.
(b)
Answer to Problem 118P
The distance of the block inclined before coming to rest is
Explanation of Solution
Write the equation (VII) from part (a) for the conservation of work –energy theorem.
Conclusion:
Substitute
Therefore, the distance of the block inclined before coming to rest is
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