PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
At a ski resort, a continuous-loop rope tow pulls skiers up a 220 m long slope that rises 45 m vertically. The rope tow’s motor supplies a constant 2.8 kW of mechanical power to the moving rope. During a particular 60 s interval the number of skiers holding the rope varies as follows:
• From t=0 s to t=20 s, five skiers are attached.
• From t=20 s to t=40 s, three skiers are attached (two let go).
• From t=40 s to t=60 s, one skier (mass 75kg) remains attached; all others have reached the top and released.
Assume the rope moves at constant speed whenever skiers are attached, friction and air resistance are negligible, and each skier’s mass is 75 kg.
(a) For each of the three time intervals stated above, calculate the share of the rope’s power available to an individual skier who remains attached during that interval.
(b) Using your results from part (a), determine the rope’s constant speed during each interval.
(c) The lone remaining skier starts from the bottom of the slope at t=0 s and remains attached for the entire 60 s. Using the speeds from part (b), calculate how far up the slope the skier has traveled by the end of the 60 s interval, and state whether the skier has reached the top.
(d) Discuss one limitation of the constant-power assumption in this scenario and explain how it could affect your answer to part (c).