Horizontal spring with friction

[Ali 2]

Homework Statement

A spring with negligible mass has a constant of 105 N/m. It has been compressed horizantally with a 2 kg mass for a distance of 0.1m. If the mass has moved after release for a distance of 0.25m, what is the coefficient of kinetic friction between mass and horizontal surface.

Homework Equations

F=-kx (spring force)
f= C N, f is friction, C is the kinetic friction coefficient, and N is the force exerted on the mass by the horizontal surface

The Attempt at a Solution

 

[Gee Wiz]

i would recommend using work to solve this problem.
Work=force*distance
also work done by a spring is .5*k*x^2

 

[ap123]

Conservation of energy would be the easiest way to solve this.
What happens to the potential energy initially stored in the spring?

 

[Ali 2]

hello
ok the work done by the spring is 0.5*k*x₀² - 0.5*k*x₁²
we know that x₀=-0.1m
but what is x₁, since the 0.25m given in the question is the distance not the displacement??!?

 

[Ali 2]

ok i see what you mean ap123
the energy stored initially = the work done by the friction force
0.5*k*x0^2= C * mg * distance

 

[ap123]

Yes, you've got it :)