摩擦力与法向力成正比

Friction is indeed proportional to normal force. The formula to calculate friction is

(Force of) friction= Frictional Coefficient * Normal Force.

The frictional coefficient depends on which two materials are passing over each other, but as you would expect, is always greater than zero. The static coefficient of friction is greater than the kinetic coefficient, which is why it takes less force to keep an object in motion than to start it moving.

So the constant of proportionality is the frictional coefficient.

Say you push a 1 kg box with 5N of force to maintain a constant speed on a level surface. Assume that $g=10\frac{m}{s^2}$ (don't forget that $F_{n}=mg$). What is the frictional coefficient of the box with the floor?

Taking a look at the problem, you note that constant speed means a net force of 0N. Since friction is always opposite to the applied force, that must mean that the magnitude of the frictional force is equal to the applied force of 5N. Normal force is $1kg\cdot10\frac{m}{s^2}=10N$.

$5N=\mu_{k}\cdot10N$

$\mu_{k}$, the kinetic coefficient of friction, must equal 1/2.