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

[deezy]

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.

 

[Delphi51]

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.

 

[deezy]

Ah... so $$W_{friction} = KE_{spring} = \frac{1}{2}k \Delta x^2 = \frac{1}{2} \cdot 200 \cdot .2^2$$?

 

[Delphi51]

looks good!

 

[asteriatic]

I would approach this problem by first identifying the known variables and equations that can be used to solve for the work done by friction force. In this case, we know the spring constant (k = 200 N/m), the compression distance (Δx = 20 cm), and the distance traveled by the box (d). We also know that the box comes to a stop, so its final velocity is 0.

From the equations given, we can use the kinetic energy equation to determine the initial velocity of the box before it comes to a stop. This initial kinetic energy is equal to the work done by the spring force, which can then be used to find the work done by friction force.

Therefore, the steps to solve this problem would be:
1. Use the kinetic energy equation to find the initial velocity of the box.
2. Use the work-energy theorem to equate the work done by the spring force to the change in kinetic energy.
3. Use the work equation (W = F · d) to solve for the work done by friction force, where the force is the friction force and the distance is the distance traveled by the box.

In summary, the work done by friction force can be found by first determining the initial velocity of the box using the kinetic energy equation and then using the work-energy theorem to equate the work done by the spring force to the change in kinetic energy. Finally, the work equation can be used to solve for the work done by friction force.