Let's break down the problem.

Problem Summary:

• Figure 1: A force $F$ is applied horizontally on a box that is resting on a rough horizontal surface. If $F$ is greater than the maximum static friction, the box will slide.
• Figure 2: The force $F$ is replaced by $\frac{F}{2}$, which is now applied to the same box.

We are asked to determine which statement is true regarding the box in Figure 2.

Key Concepts:

1. Static Friction: The maximum static friction $f_{\text{static max}}$ that can act on the box is given by: $f_{\text{static max}} = \mu_s N$ where:

   • $\mu_s$ is the coefficient of static friction,
   • $N$ is the normal force, which, on a horizontal surface, is equal to the weight of the box (i.e., $N = mg$, where $m$ is the mass and $g$ is the acceleration due to gravity).

2. Sliding Condition: For the box to start sliding, the applied force must exceed the maximum static friction, i.e., $F > f_{\text{static max}}$.

Analysis:

• In Figure 1, the force $F$ is enough to overcome static friction and cause the box to slide.
• In Figure 2, the force is reduced to $\frac{F}{2}$. If this force is less than the maximum static friction $f_{\text{static max}}$, the box will not slide, and static friction will balance this applied force to prevent motion. In this case, the force of static friction would be equal to $\frac{F}{2}$.

Conclusion:

• The force of static friction will adjust to prevent motion until the applied force exceeds the static friction's maximum limit.
• Therefore, the correct statement is: "The force of static friction on the box will be equal to F/2".

Would you like more details on how static friction works or the conditions for sliding?

Follow-Up Questions:

1. What is the difference between static and kinetic friction?
2. How is the normal force related to the weight of the box?
3. Why does reducing the applied force in Figure 2 prevent the box from sliding?
4. How can the coefficient of friction be determined experimentally?
5. What happens if the surface is inclined instead of horizontal?

Tip:

Always ensure the applied force exceeds the maximum static friction to cause motion; otherwise, the static friction matches the applied force to prevent movement.