How is maximum static friction and kinetic friction related to normal force?

Answer 1

Maximum static friction and Kinetic friction are both directly proportional to the force of gravity, which acts normal to the earth's surface.

Answer 2

Both static and dynamic friction is directly related to the normal force which is the "clamping-like" force at right angles to the area of contact. With only normal force, there will be no lateral movement and the system will remain static.
The normal force multiplied by the (experimentally determined) coefficients of friction will determine 1.- the lateral force which must be applied to start movement and 2.- the lateral force that will resist movement once it has begun.

Answer 3

static friction = force exerted onto the road from your tire if you are accelerating or slowing down.

kinetic friction = force exerted onto the road from your tire if you hit the brakes so hard that the tires stop turning (screeching the tire on the asphalt).

Normal force is jst the force that the ground pushes up on your car.

The coefficiant of friction (both static and kinetic) is the fraction of the Normal Force that slows you down. The force of friction is that fraction of the Normal force.

Lets say your tires have a coefficiant of static friction 0.4 and Your car weighs 1000kg. So the Normal force on the tires is N=ma=1000kg*9.81m/s^2=9810Newtons.
Now Ff=mu*N=0.4*9810Newtons=3924Newtons.
So your static force is 3924 Newtons. This is the force needed to get your car moving.

Now lets say that the coefficiant of kinetic friction of your tire is 0.7 and your car is still 1000kg. So repeating what we did earlier gives us 6867N. This force is the minimal force it takes to ruin your tires. The traction of your tires on the road is not strong enough to withstand the force, and therefore your tires 'slip'.

Hope this helps.