In a factory it is desired to lift 2000 kg of metal through a distance of 12 m in 1 minute. Find the minimum horsepower of the engine to be used.

Explanation

To solve the problem of finding the minimum horsepower of the engine required to lift 2000 kg of metal through a distance of 12 m in 1 minute, we can follow these steps:

### Step 1: Identify the given values
- Mass (m) = 2000 kg
- Height (h) = 12 m
- Time (t) = 1 minute = 60 seconds
- Acceleration due to gravity (g) = 10 m/s² (approximate value)

### Step 2: Calculate the work done (W)
The work done in lifting an object is given by the formula:
\[ W = mgh \]
Substituting the values:
\[ W = 2000 \, \text{kg} \times 10 \, \text{m/s}^2 \times 12 \, \text{m} \]
\[ W = 240000 \, \text{Joules} \]

### Step 3: Calculate the power (P) required
Power is defined as the work done per unit time:
\[ P = \frac{W}{t} \]
Substituting the values:
\[ P = \frac{240000 \, \text{J}}{60 \, \text{s}} \]
\[ P = 4000 \, \text{W} \]

### Step 4: Convert power from watts to horsepower
1 horsepower is equivalent to 476 watts. To convert the power from watts to horsepower, we use the conversion factor:
\[ \text{Horsepower} = \frac{P}{476} \]
Substituting the power we calculated:
\[ \text{Horsepower} = \frac{4000 \, \text{W}}{476} \]
\[ \text{Horsepower} \approx 8.39 \]

### Final Answer
The minimum horsepower of the engine required is approximately **8.39 horsepower**.

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