Question

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____KJ. [The coefficient of friction between tyre of bus and road is 0.04].

Answer 1

Correct Answer: 784

For constant speed, work done by the engine \( \text{WD}_{\text{engine}} \) + work done by friction \( \text{WD}_{\text{friction}} = 0 \) (by Work-Energy Theorem). Thus, we can write: \[ \text{WD}_{\text{engine}} = -\text{WD}_{\text{friction}} = -\left[ \mu m g x \right] \] where \( \mu = 0.04 \), \( m = 500 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), and \( x = 4 \, \text{km} = 4 \times 10^3 \, \text{m} \). So,
\[ \text{WD}_{\text{engine}} = -0.04 \times 500 \times 9.8 \times 4 \times 10^3 = 784 \, \text{KJ}. \] Thus, the work done by the engine is 784 KJ.