Answer to Question #173106 in Physics for Valerie

Question

A 50-kg block is in a plane that is inclined at 30 degrees with respect to the

horizontal. What is the acceleration of the block if there is a 150 N horizontal force

applied into it causing it to move at 3 m/s up the plane? The coefficient of friction

between the block and the plane is 0.45.

Answer 1

Let's apply the Newton's Second Law of Motion:

$$F_{appl}-mgsin\theta-\mu_kmgcos\theta=ma,$$ $$a=\dfrac{F_{appl}-mg(sin\theta+\mu_kcos\theta)}{m},$$ $$a=\dfrac{150\ N-50\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot(sin30^{\circ}+0.45\cdot cos30^{\circ})}{50\ kg},$$ $$a=-5.71\dfrac{m}{s^2}.$$