Physics Help: Spring Pushing a Box

Question

If a box weighing 5kg is pushed by a spring, and the distance from the end of the spring to the opposite end of the box is 0.5m, How far does the block slide before coming to rest? The coefficient of kinetic energy is 0.2, and the spring constant is 1500 N/m.

Answer 1

It is hard to figure out the meaning of the 0.5 m from the description, especially without a picture (note Mark's comment). In any case, if you know the spring compression distance x, set

kx²/2 = mv₀²/2

and get the initial speed v₀ upon release from the spring. Since you want to come to a complete rest at a distance d under the influence of kinetic friction, you can work with

(0)² - v₀² = 2ad = 2(F/m)d = 2(-μmg/m)d ⇒

- v₀² = -2μgd

Using the result for v₀ above and given μ, you can solve for d and finish from here. But you need to make sure you start with the correct spring compression distance, which, depending on the configuration in the missing picture, may or may not be the same as the given 0.5 m.