The questions in the images involve understanding how changing the angle $\theta$ of the applied force $\vec{F}$ affects various quantities when a box is stationary or moving.

Let’s break down each quantity:

1. Horizontal component of force $F_x$:
   The horizontal component of $\vec{F}$ is $F_x = F \cos(\theta)$. If the angle $\theta$ increases, the cosine of the angle decreases, meaning that $F_x$ will decrease.

2. Frictional force $f_s$ (static friction):
   Static friction prevents the box from moving and is proportional to the normal force $f_s = \mu_s F_N$, where $\mu_s$ is the coefficient of static friction. If $\theta$ increases, $F_N$ (the normal force) decreases, and so does the static friction $f_s$. Therefore, $f_s$ will decrease.

3. Normal force $F_N$:
   The normal force $F_N$ is the force perpendicular to the surface, given by $F_N = mg - F \sin(\theta)$. As $\theta$ increases, $\sin(\theta)$ increases, leading to a reduction in $F_N$. Therefore, $F_N$ will decrease.

4. Maximum static friction $f_{s,\text{max}}$:
   The maximum static friction is $f_{s,\text{max}} = \mu_s F_N$. Since $F_N$ decreases when $\theta$ increases, the maximum static friction also decreases. So, $f_{s,\text{max}}$ will decrease.

5. Kinetic friction (if the box is sliding):
   Kinetic friction depends on the normal force as well. Since increasing $\theta$ decreases the normal force, the kinetic friction will also decrease.

Would you like further clarifications on any of these concepts?

Related Questions:

1. What would happen to $F_x$ if the applied force magnitude $F$ is increased instead of the angle $\theta$?
2. How does the coefficient of friction $\mu_s$ affect static friction?
3. How is the work done by the force $\vec{F}$ related to the angle $\theta$?
4. What happens to the motion of the box if $f_{s,\text{max}}$ becomes smaller than the applied force?
5. How would the frictional forces change if the surface were inclined?

Tip:

When analyzing force components, always separate the forces into perpendicular and parallel directions relative to the surface for easier calculation.