The basic question we want to answer is whether less energy would be expended (and less work involved) if the woman brought her groceries upstairs by making a single trip, carrying all three bags at once, or if she made multiple trips, carrying one bag at a time (or two bags on the first trip and one bag on a second trip). Work is defined as F × d, the force multiplied by distance, or ΔE, the change in energy. The change in energy experienced in this problem is a change in potential energy, so W = ΔE = mgΔh.
First scenario: one trip carrying all three bags at once
m = mass of woman + mass of groceries = 125lb + 24lb = 149lb = 67.6kg
Δh = change in elevation = 12ft × 3 = 36ft = 11.0m
W = mgΔh = 67.6kg × 9.8m/s2 × 11.0m = 7287 N m.
Carrying all three bags at once involves approximately 7,300 N m of work.
Second scenario: carrying the bags one at a time
This means that the woman will have to go up the stairs three times and down the stairs empty-handed two times.
Going up the stairs: Going down the stairs:
m = 125lb + 8lb = 133lb = 60.3kg m = 125lb = 56.7kg
Δh = 11.0m Δh = 11.0m
W = 3 × (60.3kg × 9.8m/s2 × 11.0m) + 2 × (56.7kg × 9.8m/s2 × 11.0m) = 31725 N m.
Making multiple trips, carrying one bag up the stairs each time, involves approximately 31,700 N m of work, or between 4 and 5 times as much work as making one trip involves. The obvious best choice is for the woman to carry all three bags of groceries up the stairs at once.
