Work and Energy
Beginner
mechanical energy and conservation
Source: High school physics (Chinese)
Problem
A projectile is launched and follows a trajectory, eventually returning to its original launch height.
What is the total work done by gravity throughout this process?
W_G = 0 J
Work done by gravity, a conservative force, depends only on the vertical displacement, $\Delta h = h_f - h_i$.
$$W_G = - \Delta E_p = -mg\Delta h$$Since the projectile returns to its original height, its initial height $h_i$ is equal to its final height $h_f$.
$$\Delta h = h_f - h_i = 0$$Therefore, the total work done by gravity is zero.