The diagram shows a chairlift at a ski centre. One chair carries a skier and equipment with a combined mass of 95 kg. The chair travels 420 m along the cabl...
Question 1 Report
The diagram shows a chairlift at a ski centre. One chair carries a skier and equipment with a combined mass of 95 kg. The chair travels 420 m along the cable and rises vertically by 75 m in 50 s. The electric motor takes 120 kJ of energy from its supply for this chair. Take g as 10 N/kg. Ignore changes in kinetic energy because the chair moves at constant speed. The operator wants to check the energy transfer for a busy morning.
(a) State the change in kinetic energy of the chair during the journey. [1]
(b) Calculate the weight of the skier and equipment. [2]
(c) Calculate the useful work done in raising the skier and equipment. [3]
(d) Explain why the 420 m cable distance is not used in the calculation in part (c). [2]
(e) Calculate the useful power transferred to the skier and equipment. [3]
(f) Calculate the efficiency based on the 120 kJ energy input. [3]
(g) Describe one reason why the actual input energy is greater than the useful energy increase. [1]
Answer Details
(a) The chair travels at constant speed, so its change in kinetic energy is \(0\text{ J}\). [1]
(b) \[W=mg=95\times10=950\text{ N}\] [2]
(c) \[W=\text{weight}\times\text{vertical height}=950\times75=71250\text{ J}=71.25\text{ kJ}\] [3]
(d) Only vertical movement increases gravitational potential energy. The 420 m cable distance includes horizontal movement and is not the vertical height. [2]
(e) \[P=\frac{W}{t}=\frac{71250}{50}=1425\text{ W}=1.43\text{ kW}\] [3]
(f) \[\text{efficiency}=\frac{71250}{120000}=0.594\approx59\%\] [3]
(g) Energy is dissipated by friction in the pulleys or motor, electrical resistance, or sound. [1]
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