PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A flatbed truck tows a trailer along a straight, level highway. A dynamometer attached to the hitch records a constant tension of 3.5×103N acting on the trailer. The truck travels 2.0km while the hitch makes a constant angle of 12∘ above the horizontal because of a slight upward incline of the trailer tongue relative to the road.
After this stretch of road, the truck encounters a downhill grade and the angle of the hitch tension becomes 8∘ below the horizontal while the magnitude of the tension remains 3.5×103N. The truck covers an additional 1.5km under these conditions.
Ignore all forces other than the hitch tension for the purpose of this problem.
(a) Calculate the work done on the trailer during the first 2.0km of travel.
(b) Calculate the work done on the trailer during the subsequent 1.5km of travel.
(c) Determine the net work done on the trailer over the entire 3.5km journey, stating whether the trailer gains or loses mechanical energy.
(d) The driver wants the trailer’s net gain in energy over a future trip of the same total distance to be zero while keeping the same hitch tension magnitude. Propose one quantitative change to either or both of the travel segments (distance and/or angle) that would achieve this goal, and justify how your proposed change satisfies the requirement without relying on forces not considered in this analysis.