A car experiences rolling (tractive) friction with coe�cient of friction mut = 0.0200, and turbulent-flow (bv^2) drag, with drag coefficient CD = 0.300. The car has mass (including
fuel, which is a negligible fraction of the total) M = 1000. kg and frontal cross-sectional area S = 2.00 m^2. The density of air is approximately 1.20 kg/m^3. The heat of combustion
of gasoline is approximately 36.0 MJ per liter, but when thermal and mechanical losses are considered only 20.0 percetn of this is available for the work of propulsion. Calculate the gas mileage (km/liter will do) of this car traveling on a straight, level road at a constant speed
of 30.0 m/s.
figure the car went 100km. Using the force of friction, force of wind drag, with distance,that is the work the car did on friction.
Because of efficiency, you used 5 times this amount of energy of fuel. Now figure the amount of fuel you used.
and you then have km/liter.
I don't understand very well what I have to do...What I did before was
v= P/W
P= (mu(mg)+(1/2)(CD)(rho)Sv^3)
w=36.0 MJ*20%
V=((mu(mg)+(1/2)(CD)(rho)Sv^3)/ (36x10^6 *0.2)
I plugged in the values and got .00217 L/s and then to get the gas mileage=(0.00218^-1 x30)/1000
13.84 km/L
To calculate the gas mileage of the car, we need to find the amount of work done per liter of gasoline consumed. This can be done by calculating the power required to overcome the rolling friction and drag forces.
The power required to overcome rolling friction is calculated as:
P_rolling = mut * m * g * v
where mut is the coefficient of rolling friction (0.0200), m is the mass of the car (1000 kg), g is the acceleration due to gravity (9.8 m/s^2), and v is the velocity of the car (30.0 m/s).
The power required to overcome drag force is calculated as:
P_drag = 0.5 * CD * rho * v^3 * S
where CD is the drag coefficient (0.300), rho is the density of air (1.20 kg/m^3), v is the velocity of the car (30.0 m/s), and S is the frontal cross-sectional area (2.00 m^2).
The total power required to overcome both forces is given by:
P_total = P_rolling + P_drag
The work done per liter of gasoline consumed is given by:
Work_per_liter = P_total * (1 - thermal and mechanical losses)
Given that 20% of the heat of combustion of gasoline is available for propulsion, we can calculate the work per liter as:
Work_per_liter = 0.20 * heat of combustion of gasoline
Finally, to calculate the gas mileage, we divide the distance traveled by the amount of gasoline consumed. Since the car is traveling at a constant speed of 30.0 m/s, the distance traveled can be calculated by multiplying the speed by the time traveled. Let's assume the time traveled is t seconds.
Distance_traveled = v * t
Gas_mileage = Distance_traveled / (Work_per_liter / 36.0)
Now, you can substitute the given values (mut = 0.0200, CD = 0.300, M = 1000 kg, S = 2.00 m^2, rho = 1.20 kg/m^3, v = 30.0 m/s, heat of combustion = 36.0 MJ) to calculate the gas mileage in km/liter.