Question

Q.55 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

To maintain a constant speed, the bus has to overcome the frictional force acting on it. The frictional force is given by:

F_friction = µF_N

Where µ is the coefficient of friction and F_N is the normal force acting on the bus. Since the bus is on a flat road, the normal force is equal to the gravitational force:

F_N = mg

Where m is the mass of the bus and g is the acceleration due to gravity (approximately  9.8 m/s²).

Substituting the values, we get:

F_friction = 0.04 x 500 x 9.8

F_friction = 196 N

To maintain a constant speed, the engine must exert a force equal in magnitude to the frictional force. The work done by the engine to overcome the frictional force is given by:

W = F_friction x d

Where d is the distance traveled. First, convert the distance from km to m:

\(d = 4 km \times \frac{1000m}{1km} = 4000m\)

Now, calculate the work done:

\(W = 196N \times 4000m\, W = 784000\, J\)

Convert the work done from joules to kilojoules:

\(W = \frac {784000 \,J}{1000\,J/kJ} = 784\,kJ\)

The work done by the engine of the bus to maintain a speed of 80 km/h for a 4 km distance is 784 kJ.