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Energy and hook's law

1. Homework Statement
A 205 g cube slides down a ramp starting from rest as shown in the figure below. The ramp has a 46° slope. After falling a distance of 92 cm, the cube strikes a spring of spring constant
k = 21 N/m.
Find the maximum compression of the spring when the coefficient of kinetic friction between the cube and the ramp is 0.13.
http://puu.sh/bTjhN/ed172bac4f.png [Broken]

2. Homework Equations

conservation of energy laws
f=ma

3. The Attempt at a Solution
I solved for work of friction, the work of gravity and the work of spring (d is vertical distance of 92cm and x is the distance of compression)

http://puu.sh/bTjoU/221afafc3f.png [Broken]

I then used the conservation of energy law to piece together my 3 equations
http://puu.sh/bTjw6/e9c0236b16.png [Broken]

apparently my equation didn't match with the answer's. Can someone please tell me why?? and what did I miss??
 
Last edited by a moderator:

Simon Bridge

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Looks OK to me - what was the model answer?
 

rude man

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Looks right to me also.
 
http://puu.sh/bTRBF/53f9460841.jpg [Broken]
This is the textbook answer, could it be that the textbook is misprinted???
 

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Last edited by a moderator:

rude man

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Probably a typo.
Either put a slash between μ and tan(θ) or change tan(θ) to cot(θ).
 

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