An elevator system of mass (cabin plus counterweight difference) carries additional…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

An elevator system of mass

600\,\text{kg}

(cabin plus counterweight difference) carries additional loads as described below. The shaft height is

30\,\text{m}

. The elevator completes three consecutive trips without resting: Trip 1 (up): carries an

800\,\text{kg}

load in

40\,\text{s}

. Trip 2 (down): returns empty (only the

600\,\text{kg}

system mass) in

30\,\text{s}

. Trip 3 (up): carries a

600\,\text{kg}

load in

45\,\text{s}

. Take

g = 9.8\,\text{m\,s}^{-2}

. (i) For each trip, calculate the work done by the elevator motor against gravity (state the algebraic sign where appropriate). (ii) Obtain the net mechanical work done over the complete sequence of three trips. (iii) Determine the total time elapsed. (iv) Hence compute the average power output of the motor for the entire sequence. Comment whether a motor rated at

25\,\text{kW}

is sufficient for this duty.

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