A. µk mg cos

theta

B. µk mg sin

theta

C. µs mg cos

theta

D. µs mg sin

theta

*A) µk mg costheta*

*The force of friction acting on a sliding object is: Fkineticfriction = µk*N. Because the object is sliding (as opposed to being stationary or rolling), we need µk, and not µs. C & D are eliminated. The question is reduced to determining whether the normal force is mg costheta or mg sinθ. When the surface is perfectly flat, the normal force is equal to mg. That angle is defined as 0°, so N must be equal to mg cosθ for the normal force to equal the weight, mg.*

Fkineticfriction = µk*N

Fkineticfriction = µk*mgcostheta

Fkineticfriction = µk*mg*1

----

Fkineticfriction = µk*N

Fkineticfriction = µk*mgcostheta

Fkineticfriction = µk*mg*1

----

Why is it the normal force we are looking for here? Usually when I have a problem like this, I would have used the limiting factor approach, and would have thought we were looking for when angle is 0°, then the F = 0, not mg,

*Or if angle was 90°, then the F = mg, so then it would be*

*µk mg sinθ.*