Calculating the power of a car engine

[fawk3s]

Homework Statement

The driving power of an engine is, say 30 kN. the car drives for 5 seconds with an acceleration of 10 m/s². The initial velocity is 0 m/s.
1) What does the minimum engine power need to be for this?
2) What is the power of the engine at the end of the acceleration?

Homework Equations

A=F*s
v=v₀+at
s=v₀t+at²/2
N=A/t=F*v

The Attempt at a Solution

The first part confuses me the most. You can approach this 2 different ways:
a) you find that s=125 m; then according to the formula N=F*s/t, you get that N=0,75 MW. That would be the minimum power needed to get through 125 meters with 5 seconds. But the way I see it, this would be the power if we are not dealing with acceleration.
b) You find that the final velocity of the car is v=50 m/s. According to the formula N=F*v, you get that N=1,5 MW. But isn't this also the minimum power needed for this cenario? At the end of the acceleration the car would need to have this power. So that would also be the minimum engine power so the car could do what is described in the task.

What am I missing? Which one ise correct?

Also, is the second half of the task solved by b) as well?

Thanks in advance,
fawk3s

 

[BruceW]

The question is badly worded, and confusing. Firstly, they say "The driving power of an engine is, say 30 kN" So they say power, but give a force. I think you have correctly interpreted it to mean the force the engine produces. And I think you have done part 2 correctly. I can't think of what they want for part 1... You have worked out the time average of the power. (Since force is constant, force times distance is the total work, i.e. the power integrated over time, then you have divided by total time, so you end up with the time averaged power). This doesn't really sound like 'minimum engine power', but then I can't think of any other answer for part 1 which might give them the answer they want... whatever that is..

 

[fawk3s]

From what I can understand, the "minimum" means the power the engine must be capable of achieving in order for this scenario to work. I actually think this should be the same as the part 2 has it, because if the force which the engine produces is constantly 30 kN, and at the end of the scenario the speed of the car is 50 m/s, then the power ought to be 1,5 MW. As the car needs to achieve this power in the end, this ought to be the minimum power the car MUST be capable of achieving.

Am I not right?

 

[BruceW]

yes, I would agree. But it seems weird that the two questions ask for the same thing.

 

[Nickie]

Hello fawk3s,

Thank you for providing your attempt at a solution and your questions. Let me try to clarify and expand on the concepts involved in calculating the power of a car engine in this scenario.

Firstly, the question is asking for the minimum engine power needed for the car to achieve the given acceleration and distance in the given time. This means that the engine would need to provide at least that amount of power in order for the car to perform as described. So, in your approach (a), where you calculated the power needed to cover the given distance in the given time without considering acceleration, you are correct in finding the minimum power needed for the car to move that distance in that time. However, since the question is specifically asking for the minimum engine power needed to achieve the given acceleration, your approach (b) is more appropriate.

To further explain, in order for the car to accelerate, the engine needs to provide a force (F) to overcome the inertia of the car and increase its velocity. This force is given by Newton's second law, F=ma, where m is the mass of the car and a is the acceleration. In this scenario, the car has a mass of m=30 kN/10 m/s^2 = 3,000 kg. Therefore, the force needed to accelerate the car at 10 m/s^2 is F=3,000 kg * 10 m/s^2 = 30,000 N. This is the minimum force needed, and therefore the minimum power needed, for the car to achieve the given acceleration.

To answer the second part of the question, at the end of the acceleration, the car would have reached a final velocity of 50 m/s. At this point, the engine would need to provide a power (P) to maintain this velocity. This power is given by the equation P=Fv, where F is the force needed to maintain the velocity and v is the velocity itself. So, in this case, the power needed at the end of the acceleration would be P=30,000 N * 50 m/s = 1,500,000 W = 1.5 MW.

I hope this helps clarify the concepts involved in calculating the power of a car engine. Keep up the good work in your studies!