Negative
Explanation
Work done ($W$) by a constant force is defined as the dot product of the force vector and the displacement vector. Mathematically, $W = F \cdot d \cdot \cos(\theta)$, where $F$ is the magnitude of the force, $d$ is the magnitude of displacement, and $\theta$ is the angle between the direction of the force and the direction of displacement.
Analysis:
- When an object is lifted vertically upwards, the displacement vector points upwards.
- The gravitational force acts vertically downwards (towards the center of the Earth).
- Since the displacement and the gravitational force are in opposite directions, the angle ($\theta$) between them is $180^\circ$.
- The cosine of $180^\circ$ is $-1$.
- Consequently, the work done is calculated as $W = F \cdot d \cdot (-1)$, resulting in a negative value.
Key Takeaway:
Work done by a conservative force like gravity is negative when the displacement opposes the force (ascent) and positive when the displacement aligns with the force (descent).