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 kg and it is powered by 24 batteries, each 12 V, 85 Ah . Assume that the car is driven on level roads at an average speed of 50 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.

A) Determine the horsepower required.

B) After approximately how many kilometers must the batteries be recharged?

Explanation / Answer

a 12 volt 85 amp-hr battery stores 85*12 = 1020 watt-hr.

24 of them would be 24480 watt-hrs

24480 watt-hrs * 3600 sec/hr = 881.28*10^5 Joules

In 1 km, working against a 240 N force, W = Fd = 240*1000 = 2.4*10^5 Joules/km

so the batteries will last 881.28*10^5 Joules / (2.4*10^5) Joules/km = 367.2 km (b)

At 50 km/h or 13.89 m/s and an energy usage of 2.4*10^5 Joules/km:

2.4*10^5 Joules/km * 50 km/h = 1.2*10^7 J/hour

1.2*10^7 J/hour * 1 hr/3600s = 3333.33 J/s or 3333.33 watts.

1HP = 746 watts

so 3333.33 watts = 3333.33/746 HP = 4.468 HP

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