# Potential Energy & Conservative Forces #21

In the figure below a 1.24 kg block is held at rest against a spring with a force constant k = 700 N/m.

Initially, the spring is compressed a distance d. When the block is released it slides across a surface that is frictionless, except for a section of width x = 4.85 cm that has a coefficient of kinetic friction μk = 0.357. Calculate d such that the block's speed after crossing the rough patch is 2.23 m/s.

Sorry I can't post the picture. This was how I was figuring out the problem, but that isn't working.

k ( L_1 + x)^2 - coefficient sign (u_k)mgx = 1/2mv_f^2 + mg(0)

since d= L_1 + x and F= kd

substitute values to get L_1 and then find d

That is how i was doing it but I can't figure it out. Is there a more simple explanation or way to figure out this problem? Thanks.

Doc Al
Mentor
What's "L_1 + x" supposed to be?

The spring is compressed a distance "d": What's the energy stored in it?

Except for the spring energy term, your energy equation should work fine.

I get 0.0641 m when i figure it out my way and that answer is incorrect. Maybe I am doing some math wrong, but I double checked? What answer do you get if you use my above equation?

Are you sure it is the right equation to use?

Doc Al
Mentor
First correct the spring energy term. It should be: 1/2 k d^2.

1/2kd^2 - u_k(mgx) = 1/2mv_f^2 +mg(0)

Solve for d

I got d= 0.090595