A massles spring on a frictionless incline applies a force to a 2 kg box...?

Question

Okay, a spring facing horizontally is easy. My book is inconsistent.

If a spring pushes up an incline at a 45 degree angle.

If you compress the spring 10 meters and then release...

doesn't the box slide down the "frictionless incline" and therefore when you release the spring, gravity experiences "delta mgh" during the springing-event.

When you let go of the spring, until the box is released, say the spring is compressed 10 meters.

The potential energy of the eath-gravity system increases by mgh sin 45... am I correct?

I don't have a T.A. or a professor. I am sick of getting questions wrong each time the book excludes this distance then includes it.

The qualifier in this recent problem states "The block is not attached to the spring" and this question, I'm not supposed to assume that the box slides down when you compress the spring. Why not say "the block sits and waits at the spring's relaxed position"?

Ugh! I had been getting every question correct, but now I'm tilting!!!

Answer 1

First: when you compress the spring there is a potential energy stored in it equals to 1/2*k*x*x  ( x is squared, which is the compression distance)

second: gravity does not experience potential energy but the 2 kg box does., and it's new P.E after compression is mgh sin45 as u said, but remember it depends on your reference P.E. to be +ve or -ve potential.

Remember, every time you were answering problems on horizontal, this time there is potential energy in the box due to change in vertical position.

Finally, about your last concern, you usually start your problem after the spring is released, which means that, when the spring is compressed, this is your initial condition