Answer to Question #139413 in Physics for Luney

Question

A 2 kg block is held in equilibrium on a incline of angle 60° by horizontal force F aplied in the direction. if the coefficient between block and incline is 0.3. determine the minimum value of horizontal force F.

Answer 1

Draw the free body diagram:

Write the equilibrium of forces by axes:

$$f=\mu N\\ x:f+F\text{ cos}\alpha-mg\text{ sin}\alpha=0,\\ y: N-mg\text{ cos}\alpha-F\text{ sin}\alpha=0.$$

From the equations, we have

$$F=\frac{mg(\text{sin}\alpha-\mu\text{cos}\alpha)}{\mu\text{sin}\alpha+\text{cos}\alpha}=18.5\text{ N}.$$