[Physics] Friction on cars

Question

It is known that friction is given as :
$F_{friction}=\mu F_n$ , where $F_n$ is the normal force, and $\mu$ is coefficient of friction.

For a car travelling down a hill with constant velocity, the component of the gravitational force which is parallel to the cars velocity must be equal and opposite to the frictional force, whereby the frictional force opposes the motion of the car.

However, when the car is going up the hill, for a constant velocity to be obtained, the frictional force must be going up the hill, in the same direction as the motion of the car, and equal and opposite to the gravitational force which is antiparallel to the cars velocity.

I thought friction always opposes motion?

How can a car accelerate with the same force (i.e. friction) which also causes it to slow down. If there is no friction, a car cannot accelerate?

Answer 1

Your thinking and question is good. The issue is that you seem to have misunderstood, which friction is actually present.

• Kinetic friction is present when surfaces slide (when you push the dinner table through the living room). The formula is: $$f_k=\mu_k n$$
• Static friction is present when surfaces don't slide but try to (when you push the table, but not hard enough to make it move). The formula is: $$f_s\leq\mu_s n$$

Both have a direction that counteracts sliding. Note that the latter is only a maximum formula - the value could be anything from 0 up to this value, so it is not very useful unless you know that you have the limiting case.

When an object slides over the road, we see kinetic friction. But a car doesn't slide. It's wheels roll. At the point of contact with the ground they are in fact exactly stationary. They don't slide. No kinetic friction. They stand still in that very point like the table you are pushing not hard enough to move.

Now to the specific situation of a car driving uphill:

• Is a car parked on a hill, then static friction holds on to it by pulling upwards and balancing gravity that pulls down. Naturally.
• Is a car accelerating uphill, the same is the case, but with an even stronger static friction since the car is "pulling itself forward" by gripping the ground with the wheels.