A certain freight elevator lifts a 1600 kg mass upwards 80m in 2 minutes. The el

Question

A certain freight elevator lifts a 1600 kg mass upwards 80m in 2 minutes. The elevator uses two combined mechanisms to accomplish this: a 850 kg counterweight and a motor with power P that must lift the balance of the weight.

a) What is the minimum value for P if the elevator lifts the mass at constant speed?

b) What is the minimum value for P if the elevator lifts the mass at a constant acceleration (assume it starts from rest)?

c) From this calculation, we can infer something important about a seemingly unrelated idea: fuel economy in a car. Why are people advised to keep accelerations to a minimum for fuel efficiency?

Explanation / Answer

M = 1600 kg

m = 850 kg

for constant speed, v = 40/60 m/s = 2/3 m/s

P + mg = Mg

=> P = (1600 - 850) x 9.8 = 7350 N

b) a = 2 x 80/(120)2 = 1/90 m/s2

P + mg = Mg + (M+m)a

=> P = 750 x 9.8 + 2450/90 = 7377.222 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.