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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.

In the figure, if the box is stationary and the angle θ between the horizontal and force F is increased somewhat, do the following quantities increase, decrease, or remain the same?

Explore how increasing the angle θ of an applied force on a stationary box affects the horizontal force, static friction, normal force, and kinetic friction. This physics problem involves concepts such as trigonometric components of forces, static and kinetic friction, and the role of normal force.

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