The power of a lever used to raise a 50-kg load a 10-m height in 5 s is:

Steps to Solve

1. Calculate the Work Done

The work done (W) against gravity is calculated using the formula:

$$ W = m \cdot g \cdot h $$

where:

• ( m = 50 , \text{kg} ) (mass of the load)
• ( g = 9.81 , \text{m/s}^2 ) (acceleration due to gravity)
• ( h = 10, \text{m} ) (height)

First, calculate the weight:

$$ W = 50 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 10 , \text{m} $$

2. Find the Total Work Done

Next, solving the equation gives:

$$ W = 50 \cdot 9.81 \cdot 10 = 4905 , \text{J} $$

3. Calculate the Power Required

Power (P) is defined as work done per unit time. The formula for power is:

$$ P = \frac{W}{t} $$

where:

• ( W = 4905 , \text{J} ) (work done)
• ( t = 5 , \text{s} ) (time taken)

Substituting the values gives:

$$ P = \frac{4905 , \text{J}}{5 , \text{s}} $$

4. Solve for Power

Finally, calculate:

$$ P = 981 , \text{W} $$

Since 1 kW = 1000 W, we convert this to kilowatts:

$$ P = 0.981 , \text{kW} $$

This rounds to approximately ( 1 , \text{kW} ).