Answer to Question #139697 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
a) the minimum value of F
b) the normal force of the incline on the block

Answer 1

a) According to the free body diagram and Newton's second law, find the magnitude of the force:

$$Ox:f+F \text{cos}\theta−mg \text{sin}\theta=0\\ Oy:N−mg \text{cos}\theta−F\text{sin}\theta=0.$$

The force of friction is

$$f=\mu N.$$

After substituting the force of friction, express the horizontal force. The force is

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

b) The normal force is

$$N=mg \text{cos}\theta+F\text{sin}\theta=25.8\text{ N}.$$