What is the rate of energy transfer to the lift?

Steps to Solve

1. Identify the formula for power We will use the formula for power, which is given by:

$$ P = F \times v $$

where ( P ) is power, ( F ) is force, and ( v ) is velocity.

2. Calculate the force The force acting on the lift due to gravity can be calculated using:

$$ F = m \times g $$

Where:

• ( m = 540 , \text{kg} ) (mass of the lift)
• ( g = 9.80 , \text{m/s}^2 ) (acceleration due to gravity)

Now, substituting values:

$$ F = 540 \times 9.80 $$

3. Substitute the values to find the force Let's calculate the force:

$$ F = 540 \times 9.80 = 5292 , \text{N} $$

4. Calculate the power Now that we have the force, we can substitute it back into the power equation:

$$ P = F \times v $$

This means substituting ( F = 5292 , \text{N} ) and ( v = 3.4 , \text{m/s} ):

$$ P = 5292 \times 3.4 $$

5. Calculate the power Now, performing the multiplication:

$$ P = 5292 \times 3.4 = 18096.8 , \text{W} $$

6. Convert power to kilowatts Since power is required in kilowatts (kW), we convert watts to kilowatts by dividing by 1000:

$$ P = \frac{18096.8}{1000} = 18.1 , \text{kW} $$