What is the Maximum Speed of a Porsche 944 Turbo at Full Power?

[acws337]

Homework Statement

A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1530 kg, and two-thirds of the weight is over the drive wheels. What is the speed of the Porsche at maximum power output?

Homework Equations

P=FV

The Attempt at a Solution

I calculated the maximum power by taking 70% of 217 and multiplying by 746W/hp = 113317.4W. I don't know where to go from here, since I'm not sure how to obtain a value for F, the forces doing work on the Porsche at maximum velocity. It's not simply rolling friction, since plugging in (2/3)(1530)(9.8)(.02) (.02 is the value of rolling friction listed in the text) for F yields a maximum speed of 566.8 m/s... I would think that there would also be a drag force doing work at maximum velocity, but the dimensions of a cross section of the car are not given. Any ideas on how to go about finding vmax?

 

[acws337]

Well, I found the correct answer...but it doesn't make any sense to me. Using the friction force that accelerates the car as F (2/3)(1530)(9.8)=9996N, I found v to be 11.34m/s. That seems awfully slow for a sports car and for a car at maximum velocity I didn't think that static friction would be doing work.

 

[nlightner]

I would approach this question by first defining the variables and assumptions. The power output of the Porsche's engine is given as 217 hp, but we know that only 70% of this power reaches the wheels. This means that the power output to the wheels is 217 x 0.7 = 152.9 hp. We also know that two-thirds of the weight of the car and driver is over the drive wheels, so we can calculate the weight over the drive wheels as (2/3)(1530 kg) = 1020 kg.

Next, we can use the equation P = FV to solve for the maximum speed, where P is the power output to the wheels, F is the force acting on the car, and V is the maximum speed. We can rearrange this equation to solve for V:

V = P/F

To find the force acting on the car, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). In this case, we are looking for the acceleration at maximum velocity, so we can use the maximum acceleration that the car is capable of. This is known as the maximum traction force, and it can be calculated by dividing the weight over the drive wheels by the coefficient of static friction (F = (2/3)(1530 kg)(9.8 m/s^2) / 0.02 = 458,100 N).

Now we can plug in our values into the equation V = P/F:

V = (152.9 hp)(746 W/hp) / 458,100 N = 0.249 m/s

This is the maximum speed that the Porsche can achieve at its maximum power output. However, it is important to note that this is just a theoretical calculation and there are many other factors that can affect the actual maximum speed of a car, such as air resistance and other forms of friction.