A projected electric vehicle makes use of storage batteries as its source of ene

Question

A projected electric vehicle makes use of storage batteries as its source of energy. Its mass is 1560 { m kg} and it is powered by 24 batteries, each 12 { m V}, 90 A cdot h. Assume that the car is driven on level roads at an average speed of 40 km/h, and the average friction force is 240 N. Assume 100% efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesn't need to idle.

After approximately how many kilometers must the batteries be recharged?

Explanation / Answer

Convert units: 90 ampere-hours x 3600 seconds/hour = 324,000 ampere-seconds average total voltage = 24 batteries x 12 volts/battery / 2 = 144 V Energy used by car equals total energy the batteries can output. Force x distance = avg. voltage x current x time (that is, W=Pt=IVt) Fd = IVt ; d = IVt/F = (144 V)(324,000A-s)/(240N) = 194,400m = 194.4km Notice that mass and velocity are irrelevent. Mass is excluded since we are ignoring the energy required to accelerate. Velocity is irrelevent since the batteries will run out by 194.4km, whether it takes us a few hours or all day to travel that distence.

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