A warehouse worker must raise identical crates from the floor to a storage platform…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A warehouse worker must raise identical crates from the floor to a storage platform of height h. The worker considers three different procedures.
• Method I: Lift each crate straight upward at a slow, constant speed.
• Method II: Push each crate up a rough ramp of length 3h that makes a shallow angle with the horizontal (the coefficient of kinetic friction between crate and ramp is μ).
• Method III: Load the crate onto a motorized elevator that carries it upward to height h at constant speed; the worker merely holds the crate stationary relative to the elevator while the elevator does the lifting.
Assume the ramp surface and the elevator floor remain in contact with the crate at all times, and neglect any energy losses other than those explicitly mentioned.
(a) Qualitatively compare the magnitude of the total work done by the worker on the crate for each method. Rank the methods from greatest to least total work done by the worker, indicating any ties, and justify your ranking without performing numerical calculations.
(b) For Method II, identify the forms of energy transformation that occur as the crate is moved from the bottom to the top of the ramp. Explain qualitatively where mechanical energy is conserved and where it is not.
(c) Suppose the ramp in Method II were made frictionless while all other conditions remained the same. Describe qualitatively how, if at all, this change would alter your ranking from part (a) and your explanation in part (b).