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.

I really don't know how to do this one, can someone please help me??

To solve this problem, we need to calculate the gas mileage of the car. Gas mileage is typically measured in terms of distance traveled per unit of fuel consumed, such as kilometers per liter (km/liter) in this case.

Here are the steps to solve the problem:

1. Calculate the total resistance force acting on the car. This force includes both rolling friction and drag. The formula for the total resistance force is:

F_resistance = F_rolling + F_drag

F_rolling = mu_t * N
F_drag = CD * (0.5 * rho * v^2) * S

where:
mu_t is the coefficient of rolling friction (0.0200)
N is the normal force (equal to the weight of the car, N = M * g)
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)
S is the frontal cross-sectional area of the car (2.00 m^2)
g is the acceleration due to gravity (9.8 m/s^2)

2. Calculate the power needed to overcome the resistance force. Power is the rate at which work is done, and it is calculated as the product of force and velocity:

Power = F_resistance * v

3. Convert the power into the rate of fuel consumption. Given that only 20% of the heat of combustion of gasoline is available for propulsion, we can calculate the rate of fuel consumption as:

Fuel consumption rate = Power / (0.20 * Heat of combustion)

Heat of combustion = 36.0 MJ per liter

4. Finally, calculate the gas mileage by dividing the constant speed of the car (30.0 m/s) by the fuel consumption rate.

Gas mileage = Speed / Fuel consumption rate

Remember to convert the unit of speed from m/s to km/hr and convert the fuel consumption rate to liters per kilometer.

Please note that the given problem assumes constant speed, neglects other factors such as air resistance, variations in engine efficiency, and assumes the car is in ideal conditions. Nonetheless, these calculations provide an estimated gas mileage based on the given parameters.