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

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Homework Help Overview

The problem involves a 205 g cube sliding down a ramp with a 46° slope, striking a spring with a spring constant of 21 N/m after falling a distance of 92 cm. The scenario includes considerations of kinetic friction with a coefficient of 0.13 and requires the determination of the maximum compression of the spring using conservation of energy principles.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the work done by friction, gravity, and the spring, using conservation of energy to formulate equations. They express confusion regarding discrepancies between their results and the textbook answer.

Discussion Status

Some participants affirm the original poster's approach appears correct, while others question the accuracy of the textbook answer, suggesting it may contain a typographical error. There is ongoing exploration of the assumptions made in the calculations.

Contextual Notes

Participants are discussing potential misprints in the textbook and the implications of different interpretations of the equations involving friction and slope angles.

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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??
 
Last edited by a moderator:
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Looks OK to me - what was the model answer?
 
http://puu.sh/bTRBF/53f9460841.jpg
This is the textbook answer, could it be that the textbook is misprinted?
 

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Last edited by a moderator:
Probably a typo.
Either put a slash between μ and tan(θ) or change tan(θ) to cot(θ).
 

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