Gravity & Work

What determines the work done by gravity?

The vertical height of the incline. Note: The path up the incline is of little consequence; only the vertical height is important:

Figure 64.1: Work done by gravity: In the above illustration, all variables are constant except for height - the determinant of work done by gravity as explained by equation 64.3 below.

How is work done by gravity calculated?

$W = -Fd\cos \theta$

$\Downarrow$

$$W_{Gravity} = -mgh$$ (65.3)

Where $W$ is the work in Newton-meters (N$\cdot$m), ``$-$'' is the sign convention^65.1, $mg$ is the conversion of $F$ according to Newton's second law with $g$ corresponding to the acceleration due to gravity, and $h$ is the substitution of $d\cos \theta$ (see Figure 64.1).

What is the work done by the earth on the orbiting moon?

Zero. If you draw out the vectors, the force of gravity is perpendicular to the direction of travel (i.e. tangential to the orbit) and no work is done because, by definition, for work to occur, force and displacement must be parallel to each other. See Figure 64.2 below.

Figure 64.2: Absence of work done by gravity on the orbiting moon because the angle of displacement and the force of gravity ($F_{G}$) is equal to zero ( $\cos 90^{o} = 0$).