26. Suppose a car travels 108 km at a speed of 30.0 m/s, and uses 2.0 gal of gasoline. Only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (The energy content of gasoline is about 140 MJ/gal.) (a) What is the magnitude of the force exerted to keep the car moving at constant speed

F = 777.78N

The magnitude of the force exerted to keep the car moving at constant speed is 777.78N

Explanation:

Given;

Total distance travelled d = 108km = 108000m

Speed v = 30 m/s

Gasoline used a = 2 gal

Efficiency e = 30% = 0.3

Energy content C= 140MJ/gal

Energy used in moving the car at constant speed v is ;

E = eaC = efficiency × gasoline used × Energy content

Substituting the values;

E = 0.3×2×140MJ

E = 84MJ

Force = Energy/distance

F = E/d = 84 MJ ÷ 108km = 84 × 10^6 J ÷ 108000m

F = 777.78N

The magnitude of the force exerted to keep the car moving at constant speed is 777.78N

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