The work done against gravity can be determined by multiplying the force (i.e., weight) by the distance moved and the cosine of the angle between the force and the direction of motion.

More specifically, the work done against gravity, or any force, is expressed by the equation:

In this equation, $W$ represents the work done, $F$ is the applied force, $d$ is the distance over which the force acts, and $\theta$ is the angle between the force and the direction of motion.

When discussing work done against gravity, the force in question is the weight of the object being lifted. Weight is defined as the gravitational force acting on an object and is calculated as the product of the object’s mass ($m$) and the acceleration due to gravity ($g$). Hence, in our equation, the force $F$ becomes $mg$.

The angle $\theta$ refers to the angle between the direction of the gravitational force (which acts downward) and the direction of motion. If an object is lifted straight upward, $\theta$ is $0$ degrees, resulting in $\cos \theta = 1$. Conversely, if the object is moved horizontally, $\theta$ is $90$ degrees, leading to $\cos \theta = 0$; in this case, no work is done against gravity.

Therefore, when lifting an object directly upward, the work done against gravity simplifies to:

where $W$ is the work done, $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height to which the object is lifted.

If the object is moved at an angle, it is essential to account for this angle by including the cosine of that angle in the calculation. In summary, the work done against gravity can be described as the object’s weight multiplied by the height it is lifted, adjusted for the angle of movement:

This formula succinctly captures the relationship between mass, gravitational force, distance moved, and the angle of motion.