Question

# A truck engine transmits 28 kW (27.5 hp) to the driving wheels when the truck is traveling at a constant velocity of magnitude 60 km/h (37.3 m/h) on a

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A truck engine transmits 28 kW (27.5 hp) to the driving wheels when the truck is traveling at a constant velocity of magnitude 60 km/h (37.3 m/h) on a level road. (a) What is the resisting force acting on the truck? (b) Assume that 65% of the resisting force is due to rolling friction and that the remainder is due to air resistance. If the force of rolling friction is independent of speed and the force of air resistance is proportional to the square of speed, what power will drive the truck at 30 km/h? at 120 km/h? give your answers in kilowatts and in horsepower.

2021-02-24

velocity
$$\displaystyleМ=\frac{6000}{{3600}}={1.6666}{m}$$
force
$$\displaystyle{F}=\frac{{P}}{{V}}=\frac{{28000}}{{1.6666}}={1.68}\cdot{10}^{{{3}}}{N}$$
b) The speed is lowered by a factor ofone-half, and the resisting force is lowered by a factor of(0.65+0.35/4) and sothe power at the lower speed is
$$\displaystyle{p}={28}\cdot{\left({0.5}\right)}{\left({0.65}+\frac{0.35}{{4}}\right)}={10.3}{k}{w}$$
Similarly, at the higher speed,
$$\displaystyle{p}={28}\cdot{\left({2}\right)}{\left({0.65}+\frac{0.35}{{4}}\right)}={114.8}{k}{w}$$