Final answer:
The correct force exerted by the crane on the box is 981 newtons (N), after converting the acceleration from feet per second squared to meters per second squared. The provided answers do not correctly apply unit conversions, and option B) 3,220 lb is incorrect on this basis.
Step-by-step explanation:
The force exerted by the crane on the box can be found using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, we have the mass (m) of the box as 100 kg and the acceleration (a) as 32.2 ft/s². Before the calculation, we need to convert the acceleration to meters per second squared (m/s²) because the standard unit of force in the International System of Units (SI) is the newton (N), and 1 N = 1 kg·m/s².
Since 1 foot is equivalent to 0.3048 meters, we first convert the acceleration:
32.2 ft/s² * 0.3048 m/ft = 9.81 m/s²
Then we calculate the force (F):
F = 100 kg * 9.81 m/s² = 981 N
Therefore, the correct answer is '981 N', which is not one of the options provided. However, we must also convert newtons to pounds for the given options:
981 N * 0.225 lb/N = 220.725 lb
The closest answer in pounds is B) 3,220 lb, but this appears to be a result of multiplying the mass in kilograms by the acceleration in ft/s² without unit conversion, which is not the correct method.