# Work done by friction on an incline plane

1. Mar 16, 2013

### idllotsaroms

1. The problem statement, all variables and given/known data

http://postimage.org/image/gprwhko37/

Could someone check my work to make sure I'm doing this problem correctly?
Where:
s : hypotenuse or distance
h : height
uk : coef friction

2. Relevant equations

W = F*D
Force Normal = mgcosθ
Wfriction = (uk * N) * s(distance)

3. The attempt at a solution
Solve for θ to use to find force normal
Sinθ = h / s
θ = arcsin(h/s)

Y component of weight of box = mgcos*arcsin(h/s)
Fy = may = N - mgcos*arcsin(h/s)
N = mgcos*arcsin(h/s)

Then plug N into equation Wfriction = -uk * N * s
Wfriction = -uk*mgcos*arcsin(h/s)*s

2. Mar 16, 2013

### rude man

After a few extraneous equations, the result looks right.

3. Mar 16, 2013

### idllotsaroms

Thank you Rude man, but how would I remove the extraneous equations? Could you show me an alternate shorter way to go about doing this?

Also, would I have to solve for a when using Fy = may = N - mgcos*arcsin(h/s)?

Last edited: Mar 16, 2013
4. Mar 16, 2013

see above.