Questions: Question 9 A 220-kg object is lifted at a constant speed through a height of 42 m by a crane. The crane takes a total time of 1.8 seconds to lift this object.

Solution Steps

The work done by the crane in lifting the object is given by the formula:

\[ W = m \cdot g \cdot h \]

where:

• \( m = 220 \, \text{kg} \) is the mass of the object,
• \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity,
• \( h = 42 \, \text{m} \) is the height through which the object is lifted.

Substituting the values, we get:

\[ W = 220 \cdot 9.81 \cdot 42 \]

\[ W = 90702 \, \text{J} \]

The average power required is the work done divided by the time taken. The formula for power is:

\[ P = \frac{W}{t} \]

where:

• \( W = 90702 \, \text{J} \) is the work done,
• \( t = 1.8 \, \text{s} \) is the time taken.

Substituting the values, we get:

\[ P = \frac{90702}{1.8} \]

\[ P = 50390 \, \text{W} \]

Final Answer