Halliday, Resnick & Walker — Force and Motion-II: Problem 17

17 In Fig. 6-23, a force $\vec{P}$ acts on a block weighing $45\text{ N}$. The block is initially at rest on a plane inclined at angle $\theta = 15^\circ$ to the horizontal. The positive direction of the $x$ axis is up the plane. Between block and plane, the coefficient of static friction is $\mu_s = 0.50$ and the coefficient of kinetic friction is $\mu_k = 0.34$. In unit-vector notation, what is the frictional force on the block from the plane when $\vec{P}$ is (a) $(-5.0\text{ N})\hat{i}$, (b) $(-8.0\text{ N})\hat{i}$, and (c) $(-15\text{ N})\hat{i}$?