How Is the Spring Constant Calculated from Block Compression and Friction?

[soul5]

Homework Statement

A 1.8kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 2.0m/s and compresses it a distance of 0.11m before coming to rest. The coefficent of friction between the block and the surface is 0.560. What is the force constant of the spring?

Homework Equations

Ep=1/2kx^2
Ek=1/2mv^2

The Attempt at a Solution

I used Ek=1/2mv^2 to find Ek and I got 3.6J. I can use Ff=uFn to find force friction, but I don't know what to do? help.

 

[MaZnFLiP]

Since you know the mass of the object you would also know the Force of Gravity. Since force of gravity = Normal Force whenever its perfectly horizontal, then you could use that number you got times mew to get your frictional force

 

[Moetasim]

First, we need to find the work done by the block on the spring. This can be calculated as the change in kinetic energy of the block:

W = Ek final - Ek initial
W = 0 - 3.6J
W = -3.6J

Next, we can use the work-energy theorem to relate the work done by the block on the spring to the potential energy stored in the spring:

W = Ep final - Ep initial
-3.6J = 1/2kx^2 - 0
1/2kx^2 = -3.6J

Solving for k, we get:

k = 2(-3.6J) / (0.11m)^2
k = 2936.4 N/m

Therefore, the force constant of the spring is 2936.4 N/m.