To calculate the work done by the applied force on the wrench, we can use the formula for work:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the distance moved by the object,
- \( \theta \) is the angle between the force and the direction of motion.
In this case, the applied force is acting opposite to the motion of the wrench (i.e., upward along the shelf), which means the angle \( \theta \) is 180 degrees (or \( \pi \) radians). The cosine of 180 degrees is -1.
Given:
- \( F = 1.6 , \text{N} \)
- \( d = 1.2 , \text{m} \)
- \( \cos(180^\circ) = -1 \)
Now we can plug in the values:
\[ W = 1.6 , \text{N} \cdot 1.2 , \text{m} \cdot (-1) \]
Calculating that gives:
\[ W = 1.6 \times 1.2 \times -1 = -1.92 , \text{J} \]
Thus, the work done by the applied force on the wrench is:
\[ \boxed{-1.92 , \text{J}} \]
The negative sign indicates that the work done by the applied force is in the opposite direction to the movement of the wrench.