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## Homework Statement

http://imgur.com/xIckJqW

A block of mass

*m*rests on a plane inclined at an angle θ with the horizontal. A spring with force constant

*k*is attached to the block. The coefficient of static friction between the block and plane is μ

_{s}. The spring is pulled upward along the plane very slowly.

__(a) What is the extension of the spring the instant the block begins to move?__

__(b) The block stops moving just as the extension of the contracting spring reaches zero. Express μ___{k}(the coefficient of kinetic friction) in terms of μ_{s}and θ.## Homework Equations

F = -kx

E

_{sys}= E

_{mech}+ E

_{therm}+ E

_{chem}+ E

_{other}

G.P.E.: U = U

_{0}+

*mgh*

Spring Potential Energy: U = (1/2)

*kx*

^{2}

Kinetic Energy: K = (1/2)

*mv*

^{2}

F

_{n}=

*mg*cosθ

## The Attempt at a Solution

__Solution For Part (a):____X forces:__

(-

*kx*) ,

*mg*sinθ , F

_{n}μ

_{s}

__Y forces:__

F

_{n}, F

_{g}cosθ

ƩF

_{x}= -F

_{n}μ

_{s}-

*mg*sinθ + (-

*kx*) = 0

Solve for x:

x = (-

*mg/k*)(μ

_{s}cosθ+sinθ)

__Attempt at a solution for part (b):__E

_{1}= (1/2)mv

_{0}

^{2}+ (1/2)kx

^{2}

E

_{2}=

*mgh*+ f

_{k}x

f

_{k}x = F

_{n}μ

_{k}x =

*mg*μ

_{k}xcosθ

I'm just not really sure how to go about this question at all. I'm unsure about assuming that there is an initial velocity, but i'm basing that on the previous problem.