Kinetic and static friction on a slope

[gene_pool]

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Is the static friction of a block on an inclined slope the same formula as the kinetic friction of the box moving down the slope?

I was thinking that the static friction would be mgcos(theta) (the normal force). and then the kinetic friction would be the opposite of the direction of the box's movement: -mgsin(theta)

Is this correct? or are they both mgcos(theta)?

For example, if I was looking at work done on the box, would I use sintheta or cos theta?

 

[Cawolf]

They are both the product of the normal force and the coefficient of friction, so (mu)*(mgcostheta) in both cases.

If you want the work done on the box it really depends on the problem. Mgsin(theta)*D will correspond to the work done by gravity.

 

[gene_pool]

Okay thanks that helps. so then work done by friction (on the slope) would be the mu*mgcos(theta)*D ?

 

[Cawolf]

That would be the work of kinetic friction, as the box is sliding - so yes.

There are easier ways to find work, but that is accurate. It is hard to offer suggestions outside the context of a problem though.