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??
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 calculate the gas mileage of the car, we need to determine the amount of fuel consumed and the distance traveled.
First, we need to find the power consumed by the car at a constant speed of 30.0 m/s.
The power consumed by the car can be calculated using the formula:
P = F * v
Where:
P is the power consumed (in watts),
F is the total force acting on the car (in Newtons),
v is the velocity of the car (in meters per second).
Next, we need to find the total force acting on the car. This force includes both rolling friction and drag force.
The rolling friction force can be calculated using the formula:
F_roll = mu * m * g
Where:
mu is the coefficient of rolling friction,
m is the mass of the car (including fuel),
g is the acceleration due to gravity (approximately 9.8 m/s^2).
The drag force can be calculated using the formula:
F_drag = 0.5 * rho * CD * A * v^2
Where:
rho is the density of air,
CD is the drag coefficient,
A is the frontal cross-sectional area of the car,
v is the velocity of the car.
Once we have the total force acting on the car, we can substitute it back into the power formula to find the power consumed.
Finally, we can calculate the amount of fuel consumed and the gas mileage.
Fuel consumed = P * t / (efficiency * energy content of fuel)
Where:
P is the power consumed (in watts),
t is the time taken to travel a certain distance (in seconds),
efficiency is the fraction of the heat of combustion available for propulsion,
energy content of fuel is the energy released by combusting one liter of gasoline.
Gas mileage (km/liter) = Distance traveled (in km) / Fuel consumed (in liters)
Let's plug in the given values and calculate the gas mileage for the car.