- #1
icecool8
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Homework Statement
Hi Guys, I am trying to solve a classic problem involves conservation energy, spring, compression, I got my attempt and answer and I think my step was correct but the answer is different with the solution, can anyone please have look for me, any suggestions will be really appreciated.
Here is the question:
2kg block is at rest at the top of a inclined plane, spring constant is 100N/m is at the bottom of the incline, the equilibrium position of the spring is 4m from the block's position, the θ=30, the block is released at some instant in time. find out the compression of the spring if the kinetic coefficient of friction is 0.1
Homework Equations
ΔK+ΔU=-fd
Vf=√(Vi+2aΔx)
g=9.8
The Attempt at a Solution
n=mgcosθ, therefore f=μN=0.1*2*9.8*cos30=1.6974
ƩFx=mgsinθ-f=ma
a=(2*9.8*0.5-1.6974)/2=4.0513
Vf=√0+2*4.0513*4=5.69
then ΔK+ΔU=-fd (because the block slided down and contacted to the spring, the Vf become Vi, the Vf become 0)
(Kf+Uf)+(Ki+Ui)=-fd
0+0.5*100*x^2-0.5*2*5.69^2-2*9.8*sin30*x^2=-1.6974*4
x=0.797, but the answer in the solution sheet is 0.933m,
I don't know where I went wrong...