Question

2. The electric vehicle Tesla Model S has a drag coefficient of 0.24, a mass of 2100 kg, and a frontal area of 2.4 m2. The coefficient of rolling resistance of its tires is 0.01. Recall the density of air at sea level is 1.3 kg/m3. How much kinetic energy is required to overcome rolling resistance and air resistance (drag) at Autobahn speeds of 180 km/hr for a 200 km trip? How much useful energy (in MJ) and money (in USD @ $5.57/gal) could a German driver save fora 200 km trip by travelling at a more modest speed of 120 km/hr vs 200 km/hr? 3. 4. The largest available battery pack for a Tesla Model S is 90 kWh and the efficiency of the electric powertrain is 92%. Assuming constant travel at 120 km/hr and no other uses for electricity other than propulsion (not realistic, see part d), how far can the car go? 5. The onboard electronics uses 0.25 kWh per hour that the car is operating, regardless of speed (a simplifying assumption). Now how far can the car go? Hint: account for energy used for electronics as a function of distance travelled; be sure to stay in SI units (m, J, N)! 6. The efficiency of a conventional internal combustion engine (ICE) powertrain is about 25% (accounting for heat losses during combustion and friction in the gears, differentials, etc.) A typical gas tank size is 90 liters (Sl units, we are in Germany!). Using information on the enthalpy of gasoline (from the slides, book, or problem 3), calculate how far a gasoline-powered car can travel with a full tank, at the same speed of 120 km/hr. (lgnore on-board electronics and assume the gas- powered car has the same coefficients of drag and friction and frontal area as the Tesla Model S in problem 4. 7. Germany used to have a large portion of its electricity generation from nuclear and brown (lignite) coal, but has recently made a major shift toward renewable sources of electricity (through a policy called Energiewende). Their national average primary to electricity conversion factor is now approximately 40% (including transmission losses). If that Tesla Model S is charged using German electricity, what is the primary energy use per vehicle-km for both the Tesla and the gasoline- powered car? Assume both cars are travelling at 120 km/hr, ignore onboard electronics, and use 85% conversion loss between primary energy in oil and final energy in the gasoline for the ICE vehicle

Answer 1

Given v = 180 km/h = 50 m/s, m = 2100 kg Because Resistive force due to rolling resistance = f times mg & Because f = 0.01 = > R_f = 0.01 times 2100 times 9.81 = 206.01 N & drag force F_D = C_D times 1/2 rho v^2 times A Because C_D = 0.24, A = 2.4 m^2, rho = 1.3 kg/m^3 = > F_D = 0.24 times 1/2 times 1.3 times 50^2 times 2.4 = 936 N So, Total force to overcome = 936 + 206.01 = 1142.01 N = > Kinetic energy required = F times d = 1142.01 times (200 times 1000) J = 2.28402 times 10^8 J