# 5. The right end of a spring with spring constant k = 8N m is located a distance d =

###### Question:

5. The right end of a spring with spring constant k = 8N m is located a distance d = 2m to the left of a plane inclined at an angle θ 30°. A small block, which we can treat as a point mass. has a mass m 4kg is placed at the very top of the inclined plane and the inclined plane has a length L-3m a) First assume there is no friction between the block and the floor. What is the speed of the block after it reaches the bottom of the inclined plane but before it reaches the spring? How far will the spring compress when the block comes to a stop? How much work did the spring do on the block and how is this related to the work done by gravity when the block is on the inclined plane? b) Once the block comes to a stop, the spring will push the block to the right. How far up the ramp will the block travel before coming to a stop? c) Now suppose there is friction between the block and the inclined plane and there is also friction between the block and the horizontal part of the floor except in the region occupied by the spring (so there is friction everywhere to the right of the right end of the spring). For sinplicity let's assume μ8 ,4k and μκ 0.1 for both the inclined plane and the horizontal floor. The block is again placed at the top of the incined plane and starts from rest. Will the block reach the spring before stopping? If so, determine how far the spring is compressed when the block comes to a stop and, once the spring starts to push the block to the right, determine the final location of the block when it again comes to a stop d) Now consider the same scenario as part c), except there is also friction in the region occupied by the spring (so there is friction everywhere, and the coefficient of friction is the same ever where . Again use Į4 μ 0.1 In this case, how far does the spring compress when the block comes to a stop?

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