A car engine has 90 kW and an efficiency of 12 percent. Let's assume a simple model of air friction, Fair=Kv2 , with K=027kgm for this car. If there is no other friction, and no winds, what is the maximum speed it can reach?
To determine the maximum speed the car can reach, we need to consider the balance between the power output of the engine and the power required to overcome air friction.
First, let's calculate the power required to overcome air friction. The equation for air friction is Fair = Kv^2, where K is a constant for the car and v is the velocity.
The power required to overcome air friction can be calculated using the equation Pfriction = Fair * v. Since Fair = Kv^2, Pfriction = K * v^3.
Now, let's consider the power output of the engine. It is given that the engine has a power output of 90 kW (kilowatts) and an efficiency of 12 percent. Efficiency is defined as the ratio of useful output power to the input power. In this case, the useful output power is 90 kW * (12/100) = 10.8 kW.
Therefore, the power available for overcoming air friction is 10.8 kW.
To find the maximum speed, we need to equate the power required to overcome air friction with the power available from the engine.
Pfriction = Pengine
K * v^3 = 10.8 kW
Now, we can substitute the value of K (0.27 kg/m) and solve for v:
0.27 * v^3 = 10.8
v^3 = 10.8 / 0.27
v^3 = 40
Taking the cube root of both sides, we get:
v = 3.448 m/s
Therefore, the maximum speed the car can reach is approximately 3.448 meters per second.