Question

Calculate the horse power of the motor of an elevator, which can carry 10 persons of average mass 60 kg, through a vertical height of 20 m in 30 seconds. [Take g = 10 ms^-2 and 1 HP = 750 W]

Answer 1

Step 1: Given data:

Average mass of a person is m = 60 kg.

Vertical height is h = 20 m.

Time duration is t = 30 sec.

Total number of persons is n = 10.

Acceleration due to gravity is g = 10 m/s²

Step 2: Finding the energy consumed in carrying 1 person:

Energy required by motor to take to height h = Potential energy at height h

E = mass x acceleration due to gravity x height

E = (60 kg) x (10 m/s² ) x (20 m)

E = 12000 J.

Step 3: Finding the total power consumed:

Power = $\frac{\mathrm{energy}\mathrm{consumed}\mathrm{for}\mathrm{taking}\mathrm{n}\mathrm{persons}}{\mathrm{time}}$ = $\frac{\mathrm{Energy}\mathrm{consumed}\mathrm{in}\mathrm{taking}1\mathrm{person}\mathrm{x}\mathrm{number}\mathrm{of}\mathrm{persons}}{\mathrm{time}}$

P = $\frac{\mathrm{E}\mathrm{x}\mathrm{n}}{\mathrm{t}}$

Substituting the known values,

P = $\frac{(12000\mathrm{J}/\mathrm{person})\mathrm{x}(10\mathrm{person})}{(30\sec )}$ = 4000 J/s = 4000 W.

Step 4: Finding the total power consumed in horsepower:

Since, 1 HP = 750 W,

Power in terms of horsepower = $\frac{4000}{750}$= 5.33 HP.

Thus, the power of the motor is 5.33 HP.