Final answer:
The statement is True. The change in gravitational potential energy for a 2-lb mass decreasing by 40 ft with g = 32.2 ft/s² is indeed -2576 lb·ft, as the formula ΔPEg = mgh yields a negative value for a decrease in elevation. so, option A is the correct answer.
Step-by-step explanation:
To calculate the change in gravitational potential energy (ΔPEg) of a mass whose elevation decreases, we can use the formula ΔPEg = mgh, where m is the mass in pounds, g is the acceleration due to gravity, and h is the change in height in feet.
For a 2-lb mass decreasing in elevation by 40ft with g = 32.2 ft/s², the change in gravitational potential energy is calculated as follows:
ΔPEg = mgh = (2 lb) × (32.2 ft/s²) × (40 ft) = 2576 lb·ft
Since the mass is moving downward, the change in potential energy is negative, making it -2576 lb·ft. Therefore, the statement is True.
Gravitational potential energy is given by the formula PEg = mgh, where PEg is the gravitational potential energy, m is the mass, g is the acceleration due to gravity, and h is the change in height. In this case, the change in height is -40ft, the mass is 2 lb, and g is 32.2 ft/s². Therefore, the change in gravitational potential energy can be calculated as:
PEg = (2 lb) (32.2 ft/s²) (-40ft)
PEg = -2576 ft·lbf
So, the statement A. True is correct. The change in gravitational potential energy of the 2-lb mass whose elevation decreases by 40ft is -2576 ft·lbf.