A car of mass 1400 kg is travelling on a straight, horizontal road at a constant speed of 25 m s-1. The output power from the car’s engine is 30 kW.

Question 7

A car of mass 1400 kg is travelling on a straight, horizontal road at a constant speed of 25 m s^-1. The output power from the car’s engine is 30 kW.

The car then travels up a slope at 2° to the horizontal, maintaining the same constant speed.

What is the output power of the car’s engine when travelling up the slope?

A 12 kW                      B 31 kW                      C 42 kW                      D 65 kW

Reference: Past Exam Paper – March 2017 Paper 12 Q19

Solution:

Answer: C.

When the car is travelling on a horizontal road, its weight is directly downwards and does 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