How to Determine Maximum Spring Stretch for a Box on an Inclined Plane?

[just.karl]

A 2.0kg box rests on a plank that is inclined at a angle of 65 degrees above the horizontal. The upper end of the box is attached to a spring with a force constant of 360 N/m. If the coefficient of the static friction between the box and the plank is 0.22, what is the maximum amount the spring can be stretched and the box remain at rest?

I'm lost at how to go about at the problem. I started with figuring out the max static friction but I can't figure out how that would relate to the springs force constant.

 

[legrand]

If you have the max static friction you can then calculate the load required to start the box moving using the normal force, etc. This force will be in some amount of Newtons, say 200N (not correct answer). It's then a simple matter of looking at the spring and saying, "How far can I stretch the spring (or, how much load can I apply to the spring) before the box will move?"

If the required force to move was 200N and the spring rate is 360 N/m then you could stretch the spring a maximum of 200N/(360N/m) = .556m

Got it?

 

[just.karl]

So how or what equation does the max static friction force go into the equation to figure out the normal force?