A new electric car makes use of storage batteries as it source of energy. Its mass is 1300kg and it is powered 26 batteries, each 12v, 52 A-h. Assume that the car is driven on the level at an average speed of 40 km/h, and the average friction force is 240N. Assume 100% efficiency and neglect energy used for acceleration. Note that no energy is consumed when the vehicle is stopped since the engine does not need to idle. a. determine the horsepower requiredb. after approximately how many kilometers the battery must be changed?

a) Horse power required = 3.575 hp

b) The battery must be charged after approximately 225 km

Explanation:

a) Frictional force, F = 240 N

Average speed of the car = 40 km/h = 40 * (1000/3600) = 11.11 m/s

Horse power required = Power dissipated by the frictional force

Power = Force * Velocity

Power = 240 * 11.11

Power = 2666.67 Watt

746 Watt = 1 hp

2666.67 Watt = 2666.67/746

Horse power required = 3.575 hp

b)

The charge of 1 battery, Q = 52 Ah = 52 * 3600 = 187,200 C

Q = 187,200 C

For 24 batteries, Q = 24 * 187,200

Q = 4492800 C

Power consumed by the batteries, P = QV/t

P = 2666.67 W

2666.67 = (4492800 * 12)/t

t =  (4492800 * 12)/2666.67

t = 20217.575 s

Velocity = distance/time

11.11 = distance/20217.575

distance = 20217.575 * 11.11

distance = 224617.26 m

distance = 224.62 km

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west