The 100-lb block slides down the inclined plane for which the coefficient of kinetic friction is 0.25 k = . it is moving at 10ft/s when it reaches the point a, 10ft from b along the inclined plane.

find a) (2pt) the change in potential energy of the block going from a to b.

b) (3pt) the work done against friction going from a to b, and the speed of the block at b.

c) (5pt) the maximum deformation of the spring  needed to momentarily arrest (stop) the motion of the block

Once the force diagram has been made, we proceed to determine the variables we have,

So

The weight of the block (W)

Friction coefficient

Block speed,

For the balance of forces we perform summation, as well,

We can proceed to solve the energy equation as well

Solving the equation for 0, we find that the maximum deflection is x = 2.5ft

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seeing the graph would