The engine of a racing car of mass m delivers a constant power P at full throttle. Assuming that the friction drag force on the car is proportional to the velocity: Fdrag = -cv where c is a positive constant.What maximum speed can be attained by the car on level ground?
To find the maximum speed that can be attained by the car on level ground, we need to consider the balance of forces acting on the car.
We have the following forces acting on the car:
1. Thrust force (Fthrust): This is the force generated by the engine and is assumed to be constant at full throttle.
2. Friction drag force (Fdrag): This force is proportional to the velocity of the car and acts in the opposite direction of motion. It is given by Fdrag = -cv, where c is a positive constant.
At maximum speed, the total force on the car will be zero. This means that the thrust force will exactly balance the friction drag force. Mathematically, we can write this as:
Fthrust = Fdrag
Since Fdrag = -cv, we can substitute this into the equation:
Fthrust = -cv
Now, let's consider the power delivered by the engine. Power is defined as the rate at which work is done or energy is transferred. In this case, the power delivered by the engine is constant (P). Power is also the product of force and velocity. Mathematically, we can write this as:
Power (P) = Fthrust x velocity (v)
Substituting Fthrust = -cv into the equation, we get:
P = -cv x v
Now, we can solve this equation to find the maximum velocity (vmax) at which the power can be attained. Rearranging the equation, we have:
vmax = -P / (c)
Therefore, the maximum speed that can be attained by the car on level ground is given by vmax = -P / c.