lets say there is a box with a mass of 80 kg it is 0.6 m wide, 0.6 m deep, and 1.2 m high.
lest call the gravitational potential energy U then:
$$ U = -\int_{r1}^{r2}F \cdot dr $$
lets call the force that tilted the box F_t then I think ft should be:
$$F_t = ma + mgsin\theta$$
lets say F_t exerts a torque then:
$$I\frac{a}{R} = F_t $$
the gravitational potential energy a box as a function of the angle between the bottom of the box and the floor should be "(wrong)":
$$U = -Ft ( 0.6sin\theta - 0.6cos\theta)$$
my question is how to express the gravitational potential energy of the box as a function of the angle between the bottom of the box and the floor