An elevator with passengers has a total mass of `800 kg` and moves slowly a vertical distance of `20.0 m` in `10.0s`. What is the average power expended in lifting this mass ?

Options

A. `1.57xx10^(2) W`
B. `1.57xx10^(4) W`
C. `1.57xx10^(5) W`
D. `1.57xx10^(6) W`

Explanation

To solve the problem of calculating the average power expended in lifting the elevator, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the elevator (m) = 800 kg
- Distance moved vertically (d) = 20.0 m
- Time taken (t) = 10.0 s
- Acceleration due to gravity (g) = 9.8 m/s²

2. **Calculate the Weight of the Elevator:**
The weight (W) of the elevator can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 800 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 7840 \, \text{N} \]

3. **Calculate the Work Done (W_d):**
The work done in lifting the elevator can be calculated using the formula:
\[ W_d = F \cdot d \]
Here, the force (F) is equal to the weight (W) since the elevator is moving slowly (constant speed). Therefore:
\[ W_d = 7840 \, \text{N} \cdot 20.0 \, \text{m} = 156800 \, \text{J} \]

4. **Calculate the Average Power (P):**
Average power can be calculated using the formula:
\[ P = \frac{W_d}{t} \]
Substituting the values:
\[ P = \frac{156800 \, \text{J}}{10.0 \, \text{s}} = 15680 \, \text{W} \]

5. **Convert Power to Kilowatts (if necessary):**
To express power in kilowatts:
\[ P = \frac{15680 \, \text{W}}{1000} = 15.68 \, \text{kW} \]

### Final Answer:
The average power expended in lifting the elevator is **15680 W** or **15.68 kW**.

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