Question

A car with a mass of 1000kg is initially traveling along a level road at a steady speed of 20 m/s, and its engine is working at 18 kW. If the car is now traveling down a hill at the same speed of 20 m/s and experiences a resistive force of 900N and a brake force of 3100N, what is the change in the power output required from the engine?

Options:

A) The power output required from the engine remains the same at 18 kW.

B) The power output required from the engine decreases.

C) The power output required from the engine increases.

D) The change in power output cannot be determined with the given information.

Answer 1

The required engine power output decreases when the car travels down the hill at the same speed due to gravitational assistance offsetting the resistive forces, even though the total resistive force increases.

Step-by-step explanation:

The question involves determining the change in power output required from the engine when a car goes from traveling on a level road to traveling down a hill while experiencing additional forces. To maintain a steady speed, the engine's power output must counteract the total resistive force.

In the initial scenario on the level road, the car's engine power is 18 kW to maintain a constant speed of 20 m/s. When traveling down the hill, the car not only experiences a resistive force of 900N but also an additional brake force of 3100N, making the total resistive force on the car 4000N. Given the same speed, we can calculate the required power to overcome this force using the formula Power = Force x Velocity.

Since the car maintains the same speed (20 m/s) down the hill but needs to overcome a greater resistive force, the power required from the engine will decrease, because the gravitational component of the downhill slope contributes to the car's motion, partially offsetting the resistive forces. Therefore, Option B is correct; the power output required from the engine decreases.