Question

An elevator has a mass of 2,000 kg and is carrying a load of passengers with a combined mass of 250 kg. A constant friction force of 3,000 N retards the motion of the elevator. recall; P = dW/dt

a) How much power must the motor provide to lift the car at a constant speed of 4 m/s?

b) How much power is required to provide the elevator car with 9.8 m/s^2 of acceleration at 1 m/s vs 4 m/s?

Answer 1

here,

mass of elevator , m1 = 2000 kg

mass of passengers ,m2 = 250 kg

friction force , ff = 3000 N

a)

the net force required for constant speed , F = (m1 + m2) * g + ff

F = ( 2000 + 250) * 9.81 + 3000 N

F = 2.51 * 10^4 N

the power required , P = F * v

P = 1 * 10^5 W

b)

accelration , a = 9.8 m/s^2

the net force required , F = (m1 + m2) * g + ff + (m1 + m2) * a

F = ( 2000 + 250) * (9.81 + 9.81 ) + 3000 N

F = 47145 N

for v1 = 1 m/s

the power required , P1 = F * v1

P1 = 4.71 * 10^4 W

for v2 = 4 m/s

the power required , P2 = F * v2

P2 = 1.88 * 10^5 W