Work energy theorem to find the maximum compression

AI Thread Summary
To find the maximum compression of a spring using the work-energy theorem, the kinetic energy of the box before it hits the spring must be equated to the potential energy stored in the spring at maximum compression. The initial kinetic energy (K1) of the box is calculated as 27 J. At maximum compression, all kinetic energy is converted into spring potential energy, which is given by the formula U = 1/2kx^2, where k is the spring constant. The spring constant is provided as 75 N/cm, which should be converted to N/m for calculations. The solution requires setting the initial kinetic energy equal to the spring potential energy to solve for the maximum compression.
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Homework Statement


A 6.0 kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75N/cm. Use the work energy theorem to find the maximum compression of the spring.


Homework Equations


Wtotal=K2-K1

k1=1/2mv^2=27 J


The Attempt at a Solution


I mus tbe missing something conceptually here, this doesn't appaear to be a difficult problem but I just don't know how to approach it. I don't know the total work, how do I find it?
 
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Can you find the kinetic energy of the box before it hits the spring?
 
At the maximum compression the box stops
So all the initial Ke is now spring energy.
What's the equation for energy stored in a spring in terms of spring force and extention?
 

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