Question 239: Work, Energy and Power & Circular Motion

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.]

Accepted Answer

To maintain a constant speed, the bus has to overcome the frictional force acting on it. The frictional force is given by:
$$F_{friction} = \mu F_N$$
Where $$\mu$$ 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 $$9.8 \mathrm{~m/s^2}$$).
Substituting the values, we get:
$$F_{friction} = 0.04 	imes 500 	imes 9.8$$
$$F_{friction} = 196 \mathrm{~N}$$
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:
$$W = F_{friction} 	imes d$$
Where $$d$$ is the distance traveled. First, convert the distance from km to m:
$$d = 4 \mathrm{~km} 	imes \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} = 4000 \mathrm{~m}$$
Now, calculate the work done:
$$W = 196 \mathrm{~N} 	imes 4000 \mathrm{~m}$$
$$W = 784000 \mathrm{~J}$$
Convert the work done from joules to kilojoules:
$$W = \frac{784000 \mathrm{~J}}{1000 \mathrm{~J/ kJ}} = 784 \mathrm{~kJ}$$
The work done by the engine of the bus to maintain a speed of 80 km/h for a 4 km distance is $$784.8 \mathrm{~kJ}$$.

Work, Energy and Power & Circular Motion

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.]

Integer / Numeric Answer Type