What did I miss in my energy and hook's law homework calculation?

AI Thread Summary
The discussion focuses on a physics homework problem involving a cube sliding down a ramp and compressing a spring. The student calculated the work done by friction, gravity, and the spring using conservation of energy but found discrepancies with the textbook answer. Participants suggest potential errors in the textbook, such as a misprint regarding the relationship between the coefficient of friction and the angle of the ramp. They propose adjustments to the equations, including possibly using cotangent instead of tangent. The conversation highlights the importance of verifying equations and understanding the underlying physics principles.
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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

2. Homework Equations
conservation of energy laws
f=ma

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

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

apparently my equation didn't match with the answer's. Can someone please tell me why?? and what did I miss??
 
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Looks OK to me - what was the model answer?
 
Looks right to me also.
 
http://puu.sh/bTRBF/53f9460841.jpg
This is the textbook answer, could it be that the textbook is misprinted?
 

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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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