An engine develops 20 kW of power. How much time will it take to lift a mass of 400 kg to a height of 40 m? `(g=10 ms^(-2))`

Options

A. `4s`
B. `5s`
C. `8s`
D. `10s`

Answer

To solve the problem of how much time it will take for an engine that develops 20 kW of power to lift a mass of 400 kg to a height of 40 m, we can follow these steps:

### Step 1: Calculate the Work Done
The work done (W) in lifting an object can be calculated using the formula:
\[ W = m \cdot g \cdot h \]
where:
- \( m = 400 \, \text{kg} \) (mass)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 40 \, \text{m} \) (height)

Substituting the values:
\[ W = 400 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 40 \, \text{m} \]
\[ W = 400 \cdot 10 \cdot 40 \]
\[ W = 160000 \, \text{J} \]

### Step 2: Convert Power to Watts
The power (P) developed by the engine is given as 20 kW. We need to convert this to watts:
\[ P = 20 \, \text{kW} = 20 \times 10^3 \, \text{W} = 20000 \, \text{W} \]

### Step 3: Use the Power Formula to Find Time
The relationship between power, work done, and time is given by:
\[ P = \frac{W}{t} \]
Rearranging this to find time (t):
\[ t = \frac{W}{P} \]

Substituting the values we calculated:
\[ t = \frac{160000 \, \text{J}}{20000 \, \text{W}} \]
\[ t = \frac{160000}{20000} \]
\[ t = 8 \, \text{s} \]

### Conclusion
The time taken to lift the mass is \( t = 8 \, \text{s} \).

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