[10 marks] An escalator (Fig. 1) in Aeon shopping mall is designed to move 20 people...

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[10 marks] An escalator (Fig. 1) in Aeon shopping mall is designed to move 20 people (with an average mass of 90 kg) at a constant speed of 1.2 m/s at 30 slope. Assume (i) the mass of escalator is negligible, () the escalator transits steadily (without acceleration and deceleration), and frictional force can be ignored. By treating the inclined escalator as a closed system, (a) Determine the total mass that moved by the escalator at a time. [1 mark] [2 mark] (c) it is well known that energy cannot be created and destroyed, but can transform from one (b) Calculate the vertical component of escalator velocity. form to another form. Complete the energy transformation step by identify the energy (X and [2 mark] Electrical energy Mechanical energy→ X→ Y (d) Apply the energy balance equation to determine minimum power input. [Hint: Some basic [3 mark] derivation is needed] (e) Predict what will happen to the minimum power input if the escalator velocity is doubled. 12 mark] Either mathematical deduction or direct calculation is acceptable as the answer. [10 marks] An escalator (Fig. 1) in Aeon shopping mall is designed to move 20 people (with an average mass of 90 kg) at a constant speed of 1.2 m/s at 30 slope. Assume (i) the mass of escalator is negligible, () the escalator transits steadily (without acceleration and deceleration), and frictional force can be ignored. By treating the inclined escalator as a closed system, (a) Determine the total mass that moved by the escalator at a time. [1 mark] [2 mark] (c) it is well known that energy cannot be created and destroyed, but can transform from one (b) Calculate the vertical component of escalator velocity. form to another form. Complete the energy transformation step by identify the energy (X and [2 mark] Electrical energy Mechanical energy→ X→ Y (d) Apply the energy balance equation to determine minimum power input. [Hint: Some basic [3 mark] derivation is needed] (e) Predict what will happen to the minimum power input if the escalator velocity is doubled. 12 mark] Either mathematical deduction or direct calculation is acceptable as the answer.