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As an introduction this is what's written in my textbook:

$Power=\frac{work\ done\ by\ driving\ force}{time}$

$=\frac{Driving\ force×distance}{time}$

(as distance over time = speed)

$= Driving\ force×speed$

Note: If the power is constant and the body is accelerating then the speed is changing thus the driving force must also change to keep the power constant.

And in most of the questions we solved in class we assume that the power (of a car) is constant and the "note" in the text I mentioned explains how it will be constant and I understand that.

What I don't understand is why will it be constant in the first place? Shouldn't the car exert the same force all the time— so the speed will increase increasing the distance— and thus the work done will increase as time passes and the power will keep increasing?

My teacher informed us that we "assume" that the power is constant and that it variates between a certain range.

• Yet why does the power have to be limited to a certain range? Why doesn't it increase forever? Or at least increase until it comes to its maximum speed due to air resistance?

• Why does speed decrease when the driving force gets bigger even when there's no friction to prevent the car from speeding up forever?

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  • $\begingroup$ " Why does speed decrease when the driving force gets bigger even when there's no friction to prevent the car from speeding up forever? " What exactly do you mean by "driving force" in this context ? and why do you think there is no friction ? $\endgroup$ – silverrahul Apr 26 at 16:44
  • $\begingroup$ I read this question while I was writing mine on se (unfortunately I can't find it at the moment) where someone was asking about infinite power in case a car is moving on a frictionless road and in one of the answers there was sth around that the speed would decrease as the driving force increase— which shocked me because I thought it would keep accelerating forever. That's why I added my last question. $\endgroup$ – Manar Apr 26 at 17:42
  • $\begingroup$ If you mean driving force as simply the force that is pushing the car at any moment, then speed WILL NOT decrease when driving force gets bigger. If driving force gets bigger, then car will accelerate harder. $\endgroup$ – silverrahul Apr 26 at 17:45
  • $\begingroup$ Oh! So if we assume that the driving force isn't a car engine and that the driving force doesn't change by the change of speed (due to its mechanism of how it changes chemical energy into kinetic energy as Nuclear Hoagie mentioned) then our power won't be constant at any instant and we will keep accelerating for a very long time) $\endgroup$ – Manar Apr 26 at 19:14
  • $\begingroup$ yes. that is true $\endgroup$ – silverrahul Apr 26 at 20:02
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• Yet why does the power have to be limited to a certain range? Why doesn't it increase forever? Or at least increase until it comes to its maximum speed due to air resistance?

This has to do with how an internal combustion engine works.

The power generated by an engine depends on, among other factors, how well the engine can "breathe" that is whether it is getting enough air through the intake valves. As the rpm of the engine increases, it needs more and more inflow of air, but the intake valves of engines can only provide so much airflow.

Hence, as the rpm of an engine increases, its power output increases at first, but after some point, its power output starts to plateau and then decreases.

This is the reason that automobile engines can provide power only within a certain range of rpm.

As you can see in the diagram below (which shows the power curves for both a gasoline and a diesel engine), the power starts to increase with rpm , but after a certain rpm it starts to plateau and then decreases

enter image description here

For most passenger vehicles, this point is much before the maximum allowed by air resistance. But, there are many high powered supercars etc. which can reach the high speeds nearing the maximums allowed by air resistance

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  • $\begingroup$ So if that's how a car can happen to know when and by how much it changes its speed when driving force increases, what about bicycles then? I solved a problem where a cyclist is travelling with constant power and it was confusing how can a cyclist know when to decrease its speed or its force to equalise the power equation. $\endgroup$ – Manar Apr 26 at 19:48
  • $\begingroup$ Okay, bicycle is a different story. First of all, can you tell me if this answer addresses what you have asked in THIS question, or do i need to add/modify anything. I was getting the feeling that you were asking something else, in which case i would delete this answer. If a cyclist travels with constant power, then force will keep decreasing as the velocity increases. $\endgroup$ – silverrahul Apr 27 at 5:30
  • $\begingroup$ No to the very contrary, yours is one of the closest :) I asked about the mechanism or why cars engines have constant or limited power. And you explained how cars can't have unlimited power and why they move with steady power. And the automatic increase or decrease of force as speed increases to keep the power constant (which was the part that confused me the most; I couldn't get my head around how an engine knows when to decrease its driving force). $\endgroup$ – Manar Apr 27 at 15:04
  • $\begingroup$ If you meant by 'not addressing' that I was asking about the math or increase and decrease of speed that happens to keep the power constant, then no I wasn't. I've solved a lot of questions in my textbook to understand that part :) $\endgroup$ – Manar Apr 27 at 15:07
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    $\begingroup$ You have said that cyclist exerts constant power. This is something that i am taking as a given. This does not necessarily happen in the real world. But, if the question says that the cyclist is exerting constant power, then this means that he is adjusting the torque he applies on the pedals. When he starts and angular velocity of pedals is low, he applies more torque and when it becomes high, he applies less torque. This is the only way that power applied by him can remain constant. Hence, the answer to how does he know this is " he does because, that is what the question is assuming " $\endgroup$ – silverrahul Apr 27 at 15:21
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A car's engine turns the energy stored in gasoline into kinetic energy. How fast it does that is essentially the car's power (energy released divided by duration). A car engine usually takes several hours to burn a tank of gasoline, and is limited by the size of the combustion chamber, diameter of the fuel lines, air intake, and a bunch of other physical factors that limit how fast the engine burns gasoline and turns it into kinetic energy. If a car's engine had unlimited power, it would mean that you could burn an entire tank of gasoline in a fraction of a second, releasing all the energy at once and accelerating the car at an unrealistic rate. This is not possible - pressing harder on the accelerator won't make the engine suck up the entire fuel tank at once, there is some limit on how fast it can burn the gasoline. When you "floor it", the car is operating at its maximum power output, turning gasoline into kinetic energy as fast as it physically can. In most physics problems, we assume that the car is always flooring it, accelerating under the condition of maximum, constant power output.

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Power is work done per unit time. When we say there is constant power (or in a limited range) we actually mean work done increases linearly with time, that's it.

What I don't understand is why will it be constant in the first place? Shouldn't the car exert the same force all the time— so the speed will increase increasing the distance— and thus the work done will increase as time passes and the power will keep increasing?

I think you are a little confused here. "Power is constant" is a situation which we are considering here. This is the case that your book decided to cover first and this is also where we get the formula and definition for "power". When we are clear with all that we can go on to variable power and how to deal with those.

So, now we move on with the assumption that power has to remain constant.

How do we achieve that?

I think your book answers that question pretty well

If the power is constant and the body is accelerating then the speed is changing thus the driving force must also change to keep the power constant

To answer your last two questions you can consider this -

Say power is applied by the car due to which it moves forward. Now the power produces some force, and due to the force there is acceleration and that implies there is an increase in speed. The relation between speed and power is not linear, the same constant power can increase speed to a much great extent later, then what is increased in the first few seconds. But all of the increment happens if power isn't constant.

But here it is.

So some balancing will be done to keep the power constant(That is just the case we are considering for now, in your book and the example). Like if force increases speed will decrease and if speed increases force will decrease.

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  • $\begingroup$ You seem to have missed my point. I understand that constant power means work increasing linearly with time and how we manage to keep it constant (if force increases speed will decrease and if speed increases force will decrease). I was just wondering how the car will know how to do this increase or decrease and why cars have constant powers in the first place or at least a limited power range. $\endgroup$ – Manar Apr 26 at 21:41
  • $\begingroup$ We are taking a situation where power is constant, and cars don’t know how to do this, it happens automatically. For example, if a car is going very fast, since car only applies power, the force applied will automatically reduce. And if it is going very slow, then for the same power a lot of force will be applied on the body. There will be balancing between the two. This isn’t confined to cars, it will happen in any moving body, if power applied is constant. $\endgroup$ – Natru Apr 27 at 4:31
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1.Consider for a moment a car applying a force by the virtue of its internal mechanism, let just about an equal amount of force be applied on it by the force of an external factor say 'wind'. Now the car just about moves with some small speed and as it keeps covering the distance, the work done by the car keeps increasing and so does time. Hence, Power is constant.

2.Power is limited to a range as after some time it becomes impossible to match up with the passage of time. This is just the efficiency of the car at hand.

3.There is air resistance, and again energy wasted by the car's inefficiency.

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Yet why does the power have to be limited to a certain range?

Aside from the power limits of car itself, as stated in @silverrahul answer, power is limited because there is an upper limit to the driving force on the car equal to the maximum possible static friction force between the tire(s) of the drive wheel(s) and the road, which is given by

$$F_{max}=\mu_{s}N$$

where $\mu_s$ is the coefficient of static friction between the tire(s) and the road and $N$ is normal reaction force of the road on the tire(s). Once $F_{max}$ is exceeded, the tires begin to slip preventing acceleration.

Neglecting air resistance, the static friction force is the only external force acting on the car. It acts forward and is equal and opposite to the backward force of the tire on the road due to the torque applied to the wheel(s), per Newton's third law.

Hope this helps.

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  • $\begingroup$ " there is an upper limit to the driving force on the car equal to the maximum possible static friction force " What exactly does driving force mean in this context ? Is it simply the force at any moment which is pushing the car forward ? $\endgroup$ – silverrahul Apr 26 at 17:18
  • $\begingroup$ Yes I mean the force causing the car to accelerate. It is limited to the maximum static friction force between the tires and the road $\endgroup$ – Bob D Apr 26 at 17:55

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