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yuradex [85]
3 years ago
10

Suppose a car travels 108 km at a speed of 30.0 m/s, and uses 1.90 gallons of gasoline. Only 30% of the gasoline goes into usefu

l work by the force that keeps the car moving at constant speed despite friction. (The energy content of gasoline is 1.30 ✕ 108 J per gallon.)
(a) What is the force (in N) exerted to keep the car moving at constant speed? 2287.0 N
(b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s? gallons.
Physics
1 answer:
Aleksandr [31]3 years ago
7 0

Answer:

686.11 N

1.7733 gallons

Explanation:

\eta = Efficiency = 30%

V = Volume of gasoline

E = Energy content of gasoline = 1.3\times 10^8\ J/gal

F = Force

s = Displacement = 108000 m

v = Velocity

Work done is given by

W=F\times s\\\Rightarrow F=\frac{W}{s}\\\Rightarrow F=\frac{VE\eta}{s}\\\Rightarrow F=\frac{1.9\times 0.3\times 1.3\times 10^8}{108000}\\\Rightarrow F=686.11\ N

The force required to keep the car moving at a constant speed is 686.11 N

Here the force is directly proportional to speed

\\\Rightarrow F=v

\\\Rightarrow \frac{F_1}{v_1}=\frac{F_2}{v_2}\\\Rightarrow F_2=\frac{F_1\times v_2}{v_1}\\\Rightarrow F_2=\frac{686.11\times 28}{30}\\\Rightarrow F_2=640.36\ N

W=F\times s\\\Rightarrow 0.3\times 1.3\times 10^8\times V=640.36\times 108000\\\Rightarrow V=\frac{640.36\times 108000}{0.3\times 1.3\times 10^8}\\\Rightarrow V=1.7733\ gal

The gallons that will be used is 1.7733 gallons

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