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

In Fig. 6.13, 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) \((-15\text{ N})\hat{i}\)?