A car of 1400 kg is moving up a hill of slope arc sine 1/12 at a constant speed of 25m/s. If the power developed by the engine is 32 KW.Find the resistance to the motion.
Answers
not contribute in opposing the motion of the car.
In terms of energy, the engine is only providing kinetic energy.
Along the slope, a component of the weight opposes the motion of the car. Thus, the car’s engine provides both kinetic energy and gravitational potential energy since the car is gaining in height. In other words, the output power of the car’s engine should now be greater. [A incorrect]
The KE of the car remains the same as the car is moving with constant speed. So, this requires the same amount of power by the car’s engine (= 30 kW).
We need to find out the extra power required by the car on the slope.
Let the distance moved by the car along the slope be h.
Gain in height of the car on the slope is Δh sin 2
Gain in GPE = mgh sin2
Power = Energy / time = (mgh sin 2) / t
Power = mgv sin 2 since speed v = h / t
Power = 1400 × 9.8 × 25 sin2 = 12.2 kW
This is the extra power required by the car on the slope.
Total power of car’s engine = 30 + 12.2 = 42.2 kW
Hope it helps you.......
