Gradually increase the angle of the incline, but keep the angle low enough that the block does not slide. Select all the phrases below that would make the following statement true: For this situation, as the angle is increased.

a. the maximum possible value of the force of static friction stays the same
b. the force of static friction increases
c. the maximum possible value of the force of static friction increases
d. the force of static friction decreases
e. the force of static friction stays the same
f. the maximum possible value of the force of static friction decreases.

Respuesta :

Answer:

For the simplicity, I will denote the direction along the inclined plane as x-direction, and the perpendicular direction as y-direction.

A. Wrong. The maximum possible value of the force of static friction is

[tex]F_s = \mu_smg\cos(\theta)[/tex]

As the angle is increased, cosine component is decreases, so the maximum value of the static friction force decreases.

B. Correct. The force of static friction (not the maximum value) increases, as the x-component of the weight of the block increases with the angle.

[tex]w_x = mg\sin(\theta)[/tex]

C. Wrong. As I explained in part A the maximum value of the force of static friction decreases.

D. Wrong. The force of static friction (not the maximum value) increases as explained in part B.

E. Wrong. As explained in part B, the force of static friction increases.

F. Correct. As I explained in part A, the maximum value of the force of static friction decreases.