A car's engine is 20% efficient.When cruising,the car encounters an average retarding force of 1000 N.If the energy content of gasoline is 40 megajoules per liter,how many kilometers per liter does the car get?

Question

Quizplus · Accepted Answer

Given: 
- Engine efficiency = 20%
- Retarding force = 1000 N
- Energy content of gasoline = 40 MJ/L

To find: 
Number of kilometers per liter (km/L)

We can use the following formula:

Efficiency = (Work output / Energy input) x 100%

The work output is the force applied multiplied by the distance traveled (W = F x d). When cruising, the force and displacement are in the same direction. Therefore, the work output is:

Work output = Force x Distance

We don't know the distance, but we can use the fact that the retarding force is equal to the driving force when cruising at a constant speed. Therefore, we can write:

Driving force = F = 1000 N

Now, the work output becomes:

Work output = F x d = 1000 x d

The energy input is the energy content of gasoline multiplied by the engine efficiency. We convert MJ/L to J/m:

Energy input = 40 x 10^6 J/L x 0.2 = 8 x 10^6 J/L

Now, we can write:

Efficiency = (Work output / Energy input) x 100%
20 = (1000 x d) / (8 x 10^6)
d = 20 km/L

Therefore, the car gets 20 km per liter of gasoline. The closest answer choice is D: 8 km/L, which is the correct answer.

A Car's Engine Is 20% Efficient