Answer to Question #252968 in Mechanics | Relativity for Ellea

Question

 A 5.0 kg block is on a horizontal surface. The coefficient of static friction between the block and the surface is 0.6. A frame of 20 N is applied to the block and acts at an angle of 30⁰ above the horizontal. Is the block in equilibrium? Show the free-body diagram. 

Answer 1

The block will be in equlibrium if $F_{frame, x} < F_{s.fr.}.$ Let's calculate both forces:

$$F_{frame, x}=F_{frame}cos\theta=20\ N\cdot cos30^{\circ}=17.32\ N,$$ $$F_{s.fr.}=\mu_{s.fr.}N=\mu_{s.fr.}(mg-F_{frame}sin\theta),$$ $$F_{s.fr.}=0.6\cdot(5\ kg\cdot9.8\ \dfrac{m}{s^2}-20\ N\cdot sin30^{\circ})=23.4\ N.$$

As we can see from calculations, $F_{frame, x} < F_{s.fr.}$, therefore, the block is in equilibrium.