An escalator (Fig. 1) in Aeon shopping mall is designed to move 20 people (with an...

 

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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, (i) the escalator transits steadily (without acceleration and deceleration), and (ii) 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) (b) Calculate the vertical component of escalator velocity. [2 mark) (c) It is well known that energy cannot be created and destroyed, but can transform from one form to another form. Complete the energy transformation step by identify the energy (X and Y). [2 mark) Electrical energy → Mechanical energy > X > Y (d) Apply the energy balance equation to detemine minimum power input. [Hint: Some basic derivation is needed] [3 mark) (e) Predict what will happen to the minimum power input if the escalator velocity is doubled. Either mathematical deduction or direct calculation is acceptable as the answer. [2 mark] v 1.2 m/s 0 30° Fig. 1: A moving escalator that modelled as a closed system 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, (i) the escalator transits steadily (without acceleration and deceleration), and (ii) 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) (b) Calculate the vertical component of escalator velocity. [2 mark) (c) It is well known that energy cannot be created and destroyed, but can transform from one form to another form. Complete the energy transformation step by identify the energy (X and Y). [2 mark) Electrical energy → Mechanical energy > X > Y (d) Apply the energy balance equation to detemine minimum power input. [Hint: Some basic derivation is needed] [3 mark) (e) Predict what will happen to the minimum power input if the escalator velocity is doubled. Either mathematical deduction or direct calculation is acceptable as the answer. [2 mark] v 1.2 m/s 0 30° Fig. 1: A moving escalator that modelled as a closed system

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