Potential Energy & Conservative Forces #21

[UCrazyBeautifulU]

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]

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.

 

[UCrazyBeautifulU]

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]

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

 

[UCrazyBeautifulU]

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

Solve for d

I got d= 0.090595

incorrect answer

can anyone else help me with this one?

 

[Doc Al]

I got d= 0.090595

That's not the answer I get. Check your arithmetic. (Did you use the proper units for distance?)

 

[UCrazyBeautifulU]

yeah, my math was off. Thanks, i figured it out.