Question

Joe Bruin owns a Nissan Leaf electric car, but he wants to make the car even more “green” by installing solar cells on top of his electric car. Plus, in the event of a zombie apocalypse, Joe would like to be able to use his solar car to escape the zombies even after the electricity grid goes down. Joe’s car weighs 3500 lbs, and when the sun is shining overhead, the solar cells generate a total of 1000 watts of power.

a) If the battery in Joe’s car has a total energy capacity of 40 kWh, how long would it take for the solar panels to fully charge the car’s battery with the sun directly overhead and assuming no electrical losses.

b) A typical zombie can walk up a hill with a 15% slope (i.e. 1.5 meters elevation gain for every 10 meters horizontal distance traveled) at a horizontal speed of 0.5 meter per second. If Joe’s battery completely dies and he is forced to power his escape car using only solar cells (with the sun shining directly overhead and 100% efficiency), calculate if Joe should expect to be able to outrun a zombie if he encounters a hill with a 15% slope.

Hint: Calculate how fast Joe’s car can gain elevation given the power available from the solar cells. Changes in gravitational potential energy ΔPE can be calculated by the following formula: ΔPE=m g Δh, where m is the mass, g is the acceleration of gravity (9.8 m sec-2), and Δh is the change in height above the surface of the Earth.

Answer 1

a) In the case, the energy is equal to: E = Pt Where: P = 1000 W and t is the time, then: E (40 X 103)Wh = 40 h P 1000W b) The potential energy is: E mgh P=Ft Where: h=dsino then: p_mgdsino -= mgvsino Here the angle is: 0 = tan-(0.15) = 8.530 Using the giving value: P = (15568) (0.5) sin(8.53) Then: P= 1155 W Since the power required is greater than 1000 W Joe can't scape from zombies.