The power output of machine that lifts a 600 kg crate through a height of 20 m in 1 minute, is

Options

A. 0.98 kW
B. 1.96 kW
C. 3.92 kW
D. 12 kW

Answer

To find the power output of a machine that lifts a 600 kg crate through a height of 20 m in 1 minute, we can follow these steps:

### Step 1: Understand the formula for power
Power (P) is defined as the work done (W) divided by the time (t) taken:
\[ P = \frac{W}{t} \]

### Step 2: Calculate the work done
The work done in lifting the crate can be calculated using the formula:
\[ W = F \times d \]
where \( F \) is the force and \( d \) is the displacement (height in this case).

The force required to lift the crate is equal to its weight, which is given by:
\[ F = m \times g \]
where:
- \( m = 600 \, \text{kg} \) (mass of the crate)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Now, substituting the values:
\[ F = 600 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 5880 \, \text{N} \]

Now, using the height (displacement):
\[ d = 20 \, \text{m} \]

Thus, the work done is:
\[ W = 5880 \, \text{N} \times 20 \, \text{m} = 117600 \, \text{J} \]

### Step 3: Convert time from minutes to seconds
The time taken to lift the crate is given as 1 minute. We need to convert this to seconds:
\[ t = 1 \, \text{minute} = 60 \, \text{seconds} \]

### Step 4: Calculate the power
Now we can calculate the power using the work done and the time:
\[ P = \frac{W}{t} = \frac{117600 \, \text{J}}{60 \, \text{s}} = 1960 \, \text{W} \]

### Step 5: Convert power to kilowatts
To convert watts to kilowatts, we divide by 1000:
\[ P = \frac{1960 \, \text{W}}{1000} = 1.96 \, \text{kW} \]

### Final Answer
The power output of the machine is **1.96 kW**.

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