Question

. A wooden ramp has a coefficient of static friction of 0.408 and an angle of inclination of 36.2°. A 4.74 kg book is placed on the ramp. Does the book move? Show why or why not.

Answer 1

Let's apply the Newtons Second Law of Motion in projections on axis $x$ and $y$ :

$$F_{fr}-mgsin\theta=0,$$ $$N-mgcos\theta=0.$$

If the horizontal component of the book's weight will be greater than the force of friction, the book will move. Let's check that:

$$F_{fr}=\mu mgcos\theta,$$ $$F_{fr}=0.408\cdot4.74\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot cos36.2^{\circ}=15.29\ N,$$ $$W_{||}=mgsin\theta=4.74\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot sin36.2^{\circ}=27.43\ N.$$

As we can see from the calculations, $W_{||}>F_{fr}$. Therefore, the book will move.