1. The energy stored in gasoline is approximately 3.50×104 kJ per litre; 25% of

Question

1. The energy stored in gasoline is approximately 3.50×104 kJ per litre; 25% of this is converted into useful work by an automobile. When you drive on the highway at constant speed, most of the work the car does is against the drag force. Assuming there is no wind, how far can the car travel on a level road at 29.1 m/s with 15 L of gasoline? The force due to air resistance is F = Dv2, where D = 0.915, and v is the velocity in m/s.

2. If you decide to take the side roads and travel at half the speed, how far can you travel with the same amount of gas?

Explanation / Answer

First you need to know how much work is needed to overcome drag at 29.1 m/s. that work is Force of drag times distance traveled.

Fd * X

We don't know distance so we leave it as unknown X.

Dv^2* X =0.915*29.1^2*X



We want to know X for 15 L of gasoline energy. 15 liters of gasoline energy is 15 *3.5 x 10 ^4 kJ = 5* 3.5x10^7 J

Multiply this by .25, since only 25% of the energy is extracted from the total gasoline energy.
Energy = 0.25*15*3.5 x10^7 J

From the work energy theorem, work = change in energy:

Fd * X = Energy
0.915*29.1^2 * X = 0.25*15*3.5 x10^7 J

X = 169.39km

If you slow to 14.55 m/s

0.915*14.552 *X = 1.31*108

X = 677.56km

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