An escalator carries 20 passengers of average mass of 60 kg. It travels 4.2 m in height in one minute each floor. What is the minimum power for the escalator for its operation to lift these passengers from the first floor to the third floor? (Take g = 10 m `s^(-2)`)

Options

A. 840 W
B. 50400 W
C. 5040 W
D. 252 W

Answer

To solve the problem, we need to calculate the minimum power required for the escalator to lift the passengers from the first floor to the third floor. Here are the steps to find the solution:

### Step 1: Calculate the total mass of the passengers
The total mass of the passengers can be calculated by multiplying the number of passengers by the average mass of each passenger.

\[ \text{Total mass} = \text{Number of passengers} \times \text{Average mass} \]

Given:
- Number of passengers = 20
- Average mass = 60 kg

\[ \text{Total mass} = 20 \times 60 = 1200 \text{ kg} \]

### Step 2: Calculate the height the escalator needs to lift the passengers
The escalator travels a height of 4.2 m for each floor. Since we are lifting the passengers from the first floor to the third floor, we need to calculate the height for 2 floors.

\[ \text{Height} = \text{Height per floor} \times \text{Number of floors} \]

Given:
- Height per floor = 4.2 m
- Number of floors = 2

\[ \text{Height} = 4.2 \times 2 = 8.4 \text{ m} \]

### Step 3: Calculate the work done against gravity
The work done (W) to lift the passengers can be calculated using the formula:

\[ W = \text{mass} \times g \times \text{height} \]

Where:
- \( g = 10 \, \text{m/s}^2 \)

Substituting the values:

\[ W = 1200 \times 10 \times 8.4 \]

\[ W = 1200 \times 84 = 100800 \text{ J} \]

### Step 4: Calculate the time taken for the lift
The time taken for the escalator to lift the passengers from the first floor to the third floor is given as 1 minute.

Convert 1 minute into seconds:

\[ \text{Time} = 1 \text{ minute} = 60 \text{ seconds} \]

### Step 5: Calculate the power required
Power (P) is defined as the work done per unit time:

\[ P = \frac{W}{t} \]

Substituting the values:

\[ P = \frac{100800 \text{ J}}{60 \text{ s}} = 1680 \text{ W} \]

### Final Answer
The minimum power required for the escalator to lift the passengers from the first floor to the third floor is **1680 Watts**.

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