A lift of mass 920 kg has a capacity of 10 persons. If average mass of person is 68 kg. Friction force between lift and lift shaft is 6000 N. The minimum power of motor required to move the lift upward with constant velocity 3 m/s is [`g = 10 m/s^2` ]

Options

A. 66000W
B. 63248W
C. `48000W`
D. `56320`

Explanation

To find the minimum power of the motor required to move the lift upward with a constant velocity of 3 m/s, we can follow these steps:

### Step 1: Calculate the total mass of the lift with 10 persons.
- Mass of the lift = 920 kg
- Average mass of one person = 68 kg
- Number of persons = 10

Total mass of the lift with persons = Mass of the lift + (Average mass of one person × Number of persons)

\[ \text{Total mass} = 920 \, \text{kg} + (68 \, \text{kg} \times 10) = 920 \, \text{kg} + 680 \, \text{kg} = 1600 \, \text{kg} \]

### Step 2: Calculate the gravitational force acting on the lift.
- Gravitational force (weight) \( W \) can be calculated using the formula:

\[ W = m \times g \]

Where:
- \( m \) = total mass = 1600 kg
- \( g \) = acceleration due to gravity = 10 m/s²

\[ W = 1600 \, \text{kg} \times 10 \, \text{m/s}^2 = 16000 \, \text{N} \]

### Step 3: Determine the tension in the lift cable.
- The net force acting on the lift when moving at constant velocity is zero. Therefore, the tension \( T \) in the cable must balance the weight of the lift and the friction force \( F \).

\[ T - W - F = 0 \]

Where:
- \( F \) = friction force = 6000 N

Rearranging gives:

\[ T = W + F \]

Substituting the values:

\[ T = 16000 \, \text{N} + 6000 \, \text{N} = 22000 \, \text{N} \]

### Step 4: Calculate the power required to move the lift.
- Power \( P \) can be calculated using the formula:

\[ P = T \times v \]

Where:
- \( T \) = tension = 22000 N
- \( v \) = velocity = 3 m/s

Substituting the values:

\[ P = 22000 \, \text{N} \times 3 \, \text{m/s} = 66000 \, \text{W} = 66 \, \text{kW} \]

### Final Answer:
The minimum power of the motor required to move the lift upward with a constant velocity of 3 m/s is **66000 W** or **66 kW**.

---