How Far is the Second Spring Compressed When the Mass Comes to Rest?

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In summary, a 0.4 kg mass compresses a spring of constant 19 N/cm by 8 cm and then slides over a frictional surface of length 1.9 m with a coefficient of friction of 0.14. It then compresses a second spring of constant 4 N/cm on a frictionless surface. Using the conservation of energy and work energy principle, the second spring must be compressed to a distance of approximately 3.18 cm in order for the mass to come to rest.
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governergrimm
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Homework Statement


A spring of constant 19 N/cm is compressed a distance 8 cm by a 0.4 kg mass and then released on a frictionless surface. After it leaves the spring it skids over a frictional surface of length 1.9 m with coefficient of friction 0.14. Then, again on a frictionless surface, it compresses a second spring of constant 4 N/cm. The acceleration of gravity is 9.8 m/s 2 . How far must the second spring be compressed when the mass comes to rest? Answer in units of cm.

K1=19 N/m
x1=.08 m
m=.4 kg
Frictional surface = 1.9 m
μ=.14
K2=4 N/m
g=9.8

Homework Equations


Conservation of energy
work energy principle
76e1d10875eb4d0101669bcbef8c78f6.png


11e6fc84bb2641d36b09c5a6359f7c08.png


da0c6f351dc21c0fec6559f06d696174.png

N=mg
Ff=μmg

The Attempt at a Solution


http://www4c.wolframalpha.com/Calculate/MSP/MSP7167205289f8b7i74844000040h081bhh0e34g0i?MSPStoreType=image/gif&s=36&w=134.&h=35.
solve for W
W=Fs-Ff
W=K1x1-μmg

x=sqrt((K1x^2+2W)/K2)

I end up with

http://www5a.wolframalpha.com/Calculate/MSP/MSP17542240fg7bd54i8f4500000cff0b06i93i7dc9?MSPStoreType=image/gif&s=19&w=191.&h=47.
 
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  • #2
Check the consistency of your units.
 

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