Let's analyze the situation described:
1. Polly's Pushing Force:
- Polly is pushing a box to the right with a force of [tex]\(30 \, \text{N}\)[/tex].
2. Forces Acting on the Box:
- The force of gravity acting downwards is [tex]\(8 \, \text{N}\)[/tex].
- The normal force acting upwards is [tex]\(8 \, \text{N}\)[/tex].
3. Box is Not Moving:
- Given that Polly cannot move the box, it means the box is in static equilibrium. This implies that all the forces acting horizontally must balance each other out.
To achieve this balance:
- The force Polly exerts to push the box to the right is [tex]\(30 \, \text{N}\)[/tex].
- For the box to remain stationary (not moving), the force of friction, which opposes the motion, must be equal and opposite to Polly's pushing force.
Therefore, the force of friction must be exactly [tex]\( 30 \, \text{N} \)[/tex] acting to the left to balance Polly's pushing force.
Given the options:
- [tex]\( \leftarrow 30 \, \text{N} \)[/tex]
- [tex]\( \leftarrow 8 \, \text{N} \)[/tex]
- [tex]\( \rightarrow 8 \, \text{N} \)[/tex]
- [tex]\( \rightarrow 30 \, \text{N} \)[/tex]
The correct value that describes the force of friction is:
[tex]\[ \leftarrow 30 \, \text{N} \][/tex]
This indicates the force of friction is [tex]\(30 \, \text{N}\)[/tex] directed to the left.
