Question

A construction crane weighing 12,000 lbf fell from a height of 400 ft to the street below during a severe storm. For g=32.05ft/s² determine the mass, in lb, and the change in gravitational potential energy of the crane, in ft. lbf.

Answer 1

The mass of the crane is 374.1 lb, and the change in gravitational potential energy as it fell from 400 ft is 4,799,384 ft.lbf.

Step-by-step explanation:

To find the mass of the construction crane in pounds (lb), we use the relation between weight force and mass, where weight is the product of mass and acceleration due to gravity (g). The crane weighs 12,000 lbf (pound-force), and given g=32.05ft/s², mass (m) can be calculated using the formula m = weight / g. Hence, the mass of the crane is m = 12,000 lbf / 32.05 ft/s² = 374.1 lb (rounded to one decimal place).

The change in gravitational potential energy (GPE) is found with the formula GPE = mgh, where h is the height. The change in gravitational potential energy as the crane fell from 400 ft is then GPE = (374.1 lb) (32.05 ft/s²) (400 ft) = 4,799,384 ft.lbf.