Elevator

In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft
engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the counterweight.

Consider lift-enabled load Mmax = 300 kg
car weight mk = 500 kg
weight counterweight mz = 650 kg. Cabin moves at the speed
v0 = 1.2 m/s. The total efficiency of power is k =75%.

a) Explain what affects the efficiency of the system and the reason for using a counterweight.

b) Determine the power P1 engine lift if you summon an empty cabin residents of the upper floors, which moves down the speed of v0.
c) Determine the power P2 engine lift when a group of citizens with a total mass M = 250 kg conveys speed v0 upwards.

In which of these cases b), c) the need for more power?
g = gravitational constant 10 N/kg

Correct result:

P₁ =  2.4 kW
P₂ =  1.6 kW

Solution:

$$\begin{gathered} P_1=\mathrm{\mid }{m}_k-m_z\mathrm{\mid }g{v}_0{\displaystyle \frac{100}{75}} \\ {P}_1=\mathrm{\mid }500-650\mathrm{\mid }10\cdot 1.2{\displaystyle \frac{100}{75}}=2.4\text{ kW} \end{gathered}$$

$$\begin{gathered} P_2=\mathrm{\mid }{m}_k+M-m_z\mathrm{\mid }g{v}_0{\displaystyle \frac{100}{75}} \\ {P}_2=\mathrm{\mid }500+250-650\mathrm{\mid }10\cdot 1.2{\displaystyle \frac{100}{75}}=1.6\text{ kW } \\ {P}_1>P_2 \end{gathered}$$

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