Problem 65PE

Unreasonable Results

A car advertisement claims that its 900-kg car accelerated from rest to 30.0 m/s and drove 100 km, gaining 3.00 km in altitude, on 1.0 gal of gasoline. The average force of friction including air resistance was 700 N. Assume all values are known to three significant figures. (a) Calculate the car’s efficiency. (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

Part (a)

Step 1 of 6:

The speed of the car is provided. The car has gone to 100 km distance and gained 3.00 km altitude. The car must possess the kinetic and potential energy if it moves at a height. The motion of the car is affected by external resistances like friction and air resistance. We are going to find the efficiency of the car.

The mass of the car

The final speed of the car

The initial speed of the car

The height gained by the car or

The distance traveled or

The frictional force

The acceleration due to gravity

Step 2 of 6:

The efficiency of the car is the ratio of the work output and the total energy input.

The Efficiency of the car

The total energy input of 1gal of gasoline is given as

Step 3 of 6:

The work output of the car is the sum of the kinetic energy, potential energy and the work done by the frictional forces.

Substituting the known values