Question

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: (g = 9.8 m/s²)

• A. 39.2 kW
• B. 39.2 W
• C. 19.6 kW
• D. 19.6 W

Hint:

Always double-check the units in the options. 19.6 W and 19.6 kW are both present as distractors; ensure you convert Watts to kilowatts correctly by dividing by 1000.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Power is the rate at which work is done. When lifting an object, the work done is equal to the increase in the object's gravitational potential energy.

Step 2: Key Formula or Approach:
1. Work done ($W$) = $mgh$ 2. Power ($P$) = $\frac{W}{t}$

Step 3: Detailed Explanation:
Given: $m = 1000$ kg, $h = 20$ m, $t = 10$ s, $g = 9.8$ m/s². 1. Calculate Work Done: \[ W = 1000 \times 9.8 \times 20 \] \[ W = 196,000 \text{ Joules} \] 2. Calculate Power: \[ P = \frac{196,000}{10} \] \[ P = 19,600 \text{ Watts} \] 3. Convert to kilowatts (kW): \[ P = 19.6 \text{ kW} \]

Step 4: Final Answer:
The power of the crane is 19.6 kW.