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I learned that if an object is traveling at a constant velocity, then the external forces acting on the object must be in equilibrium with each other.

So, if the car is driving in a straight line at 30 miles per hour, and ignoring air resistance, then the driving force must equal the frictional force.

If the same car is driving in a straight line at 60 miles per hour, however, and ignoring air resistance, then the driving force must equal the frictional force.

But the frictional force is the same in both scenarios, because it only depends on the coefficient of kinetic friction (which is a constant) and the normal force of the car (which is constant).

This seems to imply that the driving force is constant in both scenarios. This is very counter-intuitive, because clearly there is some extra "oomph" when the car is driving at 60 miles per hour.

What is the cause for this extra "oomph"?

ComputerScienceLearner
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  • Air resistance is equals to $kv^2$, where k is the medium resistance coefficient. You can see air resistance increases exponentially. Driving force = friction + air resistance too. – QuIcKmAtHs Jan 02 '18 at 03:25
  • frictional losses in the car's transmission and differential also scale up with speed, as does flexural friction in the tires. – niels nielsen Jan 02 '18 at 03:54

2 Answers2

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While not exactly key in resolving your dilemma, note that the "frictional resistance" that occurs in this case of a body with a rolling part in constant velocity is more rolling resistance than kinetic friction. (Rolling resistance is not strictly friction, but I digress. Its mechanisms are also discussed in other questions here.)

In the two cars, one could consider all the forces acting on the car in each case. This can be done by deduction: since clearly the resistance offered by the ground is the same, the only other force that opposes the motion would be air resistance. So if one were to find that the "driving force" in the 60mph case must be greater than in the 30mph case, they must come to the conclusion that air resistance in the 60mph case is greater. Indeed this is theoretically the case; as one comment points out, the air resistance varies with the square of the velocity.

However, I'm not certain if there would actually be that great a difference in the oomph between the cases, especially on an extremely flat, long road with good tyres on a dry day.

Scripter1000
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In a perfect scenario, there will actually be no external forces doing work on the car, and therefore the car will continue at that speed forever, without the need for a driving force from the engine. On a completely flat road, there will be no difference in "oomph" from one speed to another. That "oomph" you might feel can only be due to acceleration or a placebo due to the ground moving relative to you.

In order to explain, let's imagine an idealized system with a four wheel drive car, where we ignore all non-conservative forces such as air resistance, rolling resistance etc. except for the friction between the car and the road.

If the car is not skidding along the road, it is in fact static friction (not kinetic friction) that is acting on all the wheels as either an "opposition" to the driving force of the engine or to the rolling of the wheel. This frictional force increases depending on the driving force, until it reaches a maximum, where the car might skid or "lose traction".

In our case, since the car is not skidding, the bottom point of the wheel is at zero velocity (look up "rolling without slipping"). This static friction is what actually pushes the car forward.

Now assuming these perfect conditions without a driving force from the engine, the car will in fact roll forever due to its momentum and the fact that no forces are doing work on it. Although the friction is ultimately what accelerates the car forward, it does no work as it acts at a point of zero velocity.

Now if we remove the idealizations and add back, let's say, air resistance (which is maybe how you were thinking of "kinetic friction"), then the car will of course slow down without a driving force. Therefore, the driving force does need to equal any of these frictional forces (air resistance, rolling resistance etc.) in order to keep it at the same velocity. These frictional forces tend to be higher at higher speeds, (such as air resistance, which equals $kv^2$) which will indeed mean that the driving force has to be slightly higher. But either way, if the car is traveling at a constant speed, these forces will cancel and the "oomph" should be the same.

Gary Allen
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