How much work input is required to lower (not drop) a 120 pound weight from the top of a 3 foot table to the floor?

Question

BlackTom AI · Accepted Answer

Work equals force times the vertical displacement, so W = F · d.

1) Relevant knowledge points and concepts
- In U.S. customary units, a pound (lb) when referring to weight is a unit of force (not mass). 
- Work done by a constant force through a straight-line displacement in the direction of the force is W = F × d (foot-pounds when F is in pounds and d in feet). 
- If an object is lowered at constant (slow) speed, the external agent must apply an upward force equal in magnitude to the weight; the magnitude of work the agent does while lowering through height h is F × h (sign conventions aside).

2) Step-by-step reasoning
- The weight provides a constant downward force of 120 lb.
- The vertical distance lowered is 3 ft.
- Multiply force by distance to get work (magnitude).

3) Calculations (all intermediate steps)
- F = 120 pounds
- d = 3 feet
- W = F × d = 120 lb × 3 ft
- W = 360 lb·ft (commonly written as 360 foot-pounds)

(If using sign convention for work done by the person lowering against gravity, the work done by the person is -360 ft·lb, because the person exerts an upward force while displacement is downward. The question asks for the work input required, so we give the magnitude 360 foot-pounds.)

4) Why the correct answer is correct
- The direct product of the constant force (weight) and the vertical distance yields 360 foot-pounds, matching the standard formula for work.

5) Why the other options are incorrect
- 40 foot-pounds: would correspond to 120 lb × 0.333 ft, which is not the given distance.  
- 120 foot-pounds: would correspond to lowering 1 ft (120 lb × 1 ft), not the 3 ft specified.

6) Conclusion
The computed work magnitude is 360 foot-pounds, which matches the provided correct answer: 360 foot-pounds.

How much work input is required to lower (not drop) a 120 pound weight from the top of a 3 foot table to the floor?Single choice

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