To determine the force of friction when Polly pushes the box with a force of 30 N but cannot move it, we need to analyze the situation in detail.
1. Understanding the Forces:
- Polly is pushing the box to the right with a force of 30 N.
- The force of gravity (weight) acting on the box is 8 N.
- The normal force exerted by the floor on the box is also 8 N, which balances the gravitational force.
2. Force of Friction:
- In order for Polly to not be able to move the box, the force of friction must be sufficient to counteract the 30 N of pushing force.
- This means the force of friction must be equal in magnitude but in the opposite direction of Polly's pushing force.
Therefore, the force of friction that prevents Polly from moving the box must be 30 N but acting in the opposite direction.
3. Direction of Friction Force:
- Since Polly is pushing to the right, the frictional force must act to the left to balance the pushing force.
- Thus, the force of friction is directed to the left with a magnitude of 30 N.
4. Analyzing the Answer Choices:
- [tex]$\leftarrow 30 N$[/tex]: This indicates a frictional force of 30 N acting to the left (correct choice).
- [tex]$-8 N$[/tex]: This implies a force of 8 N opposite to Polly's push, which is not sufficient to counteract her 30 N push.
- [tex]$\rightarrow 8 N$[/tex]: This indicates a force of 8 N in the direction of Polly's push, which is not correct.
- [tex]$\rightarrow 30 N$[/tex]: This indicates a force of 30 N in the same direction as Polly's push, which is not correct.
Thus, the correct value that describes the force of friction when Polly could not move the box is [tex]\(\leftarrow 30 N\)[/tex].
