ice-skating

Why we skate on the ice, why not cement? Everyone knows the answer: it is because the ice has less friction. Now, let me use the equation to prove this point.

We already learn the equation for the friction: F = μ * normal force.
What is μ?
μ is the coefficient and is a constant for any two materials in contact. We can calculate by using the equation the friction/normal force.
For ice,μ is about 0.05. If we assume the normal weight of an adult is 70kg.

Then we use the equation: Fg = M*g Fg = 70*9.8 = 686N. 
According to the Newton first law, for every action, there is an equal and opposite reaction. When human's weight gave a force to the ground, the ground also gives the human a same amount of force. We can see the normal force of human should be equal to his weight, which is also 686N. 

Now, we can calculate the static friction when an adult stands on the ice. 
We use normal force which is 686N times by mu of ice, which is 0.05. And we can get the answer 34.3N.
However, it is the static friction. It means you need 34.4N to push a man so that he can move. Nobody wants to have 34.4N while they are ice-skating because it is too much work.
In fact, while friction will decrease to about 15N which make us can easily to skate.