# Energy and hook's law

1. Sep 29, 2014

### homo-sapiens

1. The problem statement, all variables and given/known data
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. Relevant 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: May 7, 2017
2. Sep 29, 2014

### Simon Bridge

Looks OK to me - what was the model answer?

3. Sep 30, 2014

### rude man

Looks right to me also.

4. Sep 30, 2014

### homo-sapiens

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: May 7, 2017
5. Sep 30, 2014

### rude man

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