## Explanation

### Understanding Gravitation's Work

When discussing whether gravitation always does negative work, it's important to grasp the concept of work in the context of physics. **Work** is defined as the force applied to an object times the displacement of that object in the direction of the force:

In this equation:

- $W$ is the work done.
- $\vec{F}$ is the force vector.
- $\vec{d}$ is the displacement vector.
- $\theta$ is the angle between the force and displacement directions.

### Gravitational Work: Positive or Negative

Gravity is a **conservative force**, meaning the work it does only depends on the initial and final positions of the object, not on the path taken. The work done by gravity is typically calculated when an object moves within a gravitational field.

### Gravitational Force and Work

For an object of mass $m$ near the Earth's surface, subjected to gravitational force $\vec{F_g}$:

$\vec{F_g} = m \cdot \vec{g}$where $\vec{g}$ is the acceleration due to gravity.

### Scenarios when Gravity Does Negative Work

Gravity does **negative work** when the displacement of the object is **against** the direction of the gravitational force.

**Lifting an Object**: When you lift an object upwards, the displacement ($\vec{d}$) is opposite to the gravitational force ($\vec{F_g}$), with $\theta = 180^\circ$: $W_{\text{gravity}} = F_g \cdot d \cdot \cos(180^\circ) = - F_g \cdot d$ In this case, work done by gravity is negative.

### Scenarios when Gravity Does Positive Work

Gravity can **do positive work** when the displacement is in the **same** direction as the gravitational force.

**Falling Object**: When an object falls freely, the displacement is in the direction of the gravitational force, with $\theta = 0^\circ$: $W_{\text{gravity}} = F_g \cdot d \cdot \cos(0^\circ) = F_g \cdot d$ Here, the work done by gravity is positive.

### Conclusion

Gravitational work is not **always** negative. The work done by gravitational force can be **positive** or **negative** depending on the **direction of displacement** relative to the gravitational force.