How much power must a motor deliver to lift the elevator and its passengers at a constant speed of 3 m/s?, b) What power must the motor deliver at the ..........

Question

An elevator car has a mass of 1600kg and is carrying passengers with a combined mass of 200kg. A constant friction force of 4000N retards its motion.

a) How much power must a motor deliver to lift the elevator and its passengers at a constant speed of 3 m/s?

b) What power must the motor deliver at the instant the speed of the elevator is v if the motor is designed to provide the elevator car with an upward acceleration of 1 m/s^2?

Answer 1

a) F = (M + m)g + F_fr = 1800kg·9.8 m/s² + 4000 N = 21640 N

Power: P = Fv = 21640 N ·3 m/s = 64920 W

b) F_b = F + (M + m)a = 21640 N + 1800 kg·1 m/s² = 23440 N

Power: P_b = F_bv = 23440 N ·3 m/s = 70320 W

P_b is power at moment when elevator riched v = 3 m/s