# Driving and Frictional Force on a Car

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"?

• 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 2 '18 at 3:25
• frictional losses in the car's transmission and differential also scale up with speed, as does flexural friction in the tires. – niels nielsen Jan 2 '18 at 3:54

## 1 Answer

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.