2.3.15 | revision #20447 | Savchenko Solutions

Statement

2.3.15. What minimum work must be done to raise a long uniform pole of length $$l$$ and mass $$m$$ lying on the ground to a vertical position?

Solution

For a uniform pole, its center of mass is located exactly in the middle. When lying on the ground, the height of its center of mass is $$0$$ . When placed vertically, the center of mass is raised to a height of $h = \frac{l}{2}$ .

The minimum work done is equal to the increase in the potential energy of the center of mass:
$A = mgh = mg\frac{l}{2}$

Answer

$A = mg\frac{l}{2}$