A construction crew must raise identical steel beams
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A construction crew must raise 10 identical steel beams, each of weight 2.5×103N, from ground level to the top of a building 20m high. They consider the following four plans:
Plan I: A single crane lifts each beam steadily, taking 40s per beam.
Plan II: Two identical cranes work together on each beam and complete a lift in 25s.
Plan III: A temporary ramp is built so that each beam is hauled up the incline by a winch at constant speed in 60s; the displacement along the ramp is 30m.
Plan IV: A powerful crane lifts two beams at a time, completing each double lift in 55s.
(i) Assuming the work done in each plan is only against gravity (neglect friction on the ramp), calculate the average power required for one lift in each plan.
(ii) Rank the four plans from highest to lowest average power requirement, showing all working.
(iii) The site manager argues that Plan III demands least power because the speed along the ramp is lowest. Identify and correct the misconception in this reasoning.