How Do You Calculate the Coefficient of Kinetic Friction on a Slide?

[just.karl]

A child goes down a playground slide with an acceleration of 1.16m/s^2. Find the coefficient of kinetic friction between the child and the slide if the slide is inclined at an angle of 31.0 degrees below the horizontal.

I know F_k =M_k(N) is used somewhere but I'm lost otherwise where to start.

 

[Pythagorean]

start with a free body diagram and tell me what forces are on each side of it.

remember to put the direction of gravity relative to your diagram.

 

[just.karl]

I have kinetic friction going to the left proportional to x y coordinates on the free body diagram. Natural force N going vertical with y. The weight at 31 degrees below x downward.

 

[Pythagorean]

I think you mean the normal force. So... what do you get for the normal force?

 

[just.karl]

Sorry yes I do mean normal force. I've figured out the problem since. Thanks for your help anyways.

This is what I'm stuck on right now.
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.

 

[Pythagorean]

does Hooke's Law help any?