How Is Work Done by Friction Calculated in a Spring-Box System?

AI Thread Summary
The work done by friction in a spring-box system can be calculated by equating the initial spring energy to the work done by friction. The spring's potential energy is given by the formula KE_spring = (1/2)k(Δx)^2, where k is the spring constant and Δx is the compression distance. For a spring constant of 200 N/m compressed by 20 cm, the initial energy is 4 J. This energy is converted into heat by the friction force, which ultimately brings the box to a stop. Thus, the work done by friction equals the initial energy stored in the spring.
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Homework Statement


A horizontal spring with spring constant 200 N/m is compressed 20 cm and used to launch a box across a rough horizontal surface. After traveling a distance it stops. What is the work done by friction force?

Homework Equations


W = F \cdot d
KE_{spring} = \frac{1}{2}k \Delta x^2

The Attempt at a Solution


I don't know where to start, because I'm not sure what other relevant equations I can use. I'm thinking that the friction has to do enough work to make the box stop (v = 0). But I don't know how to relate the work by friction to the energy of the spring.
 
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Initially you have the spring energy. It gets converted into kinetic energy. That gets converted into heat by the work of friction. All your initial energy is equal to the work of friction.
 
Ah... so W_{friction} = KE_{spring} = \frac{1}{2}k \Delta x^2 = \frac{1}{2} \cdot 200 \cdot .2^2?
 
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looks good!
 

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