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 μs. 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 μk (the coefficient of kinetic friction) in terms of μs and θ.
F = -kx
Esys = Emech + Etherm + Echem + Eother
G.P.E.: U = U0 + mgh
Spring Potential Energy: U = (1/2)kx2
Kinetic Energy: K = (1/2)mv2
Fn = mgcosθ
The Attempt at a Solution
Solution For Part (a):
(-kx) , mgsinθ , Fnμs
ƩFx = -Fnμs - mgsinθ + (-kx) = 0
Solve for x:
x = (-mg/k)(μscosθ+sinθ)
Attempt at a solution for part (b):
E1 = (1/2)mv02 + (1/2)kx2
E2 = mgh + fkx
fkx = Fnμkx = mgμkxcosθ
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.