FRICTION

          When an object is in contact with a surface, the surface exerts a contact force on the object. The component of the contact force that's parallel to the surface is called the friction force on the object. Friction, like the normal force, arise from electrical interactions between atoms that make up the object and those that make up the surface. 
      we'll look at two main categories of friction: (1) static friction and (2) kinetic (sliding) friction. If you attempt to push a heavy crate across a floor, at first you meet with resistance, but then you push hard enough to get the create moving. The force that acted on the crate to cancel out your initial pushes was static friction, and the force that acts on the create as it sides across the floor is kinetic friction. static friction occurs when there is no relative motion between the object and the surface ( no sliding); kinetic friction occurs when there is relative motion )when there's sliding).
     The strength of the friction force  depends, in general, on two tho things: the nature of the surface and the strength of the normal force. The nature of the surfaces is represent by the coefficient of friction, denoted by μ (mu). The greater this number is, the stronger the friction force will be. For example, the coefficient or friction between rubber-soled shoes and a wooden floor is 0.7, but between rubber-soled shoes and ice, it's only 0.1. Also, since kinetic friction is generally weaker than static friction (it's easier to keep an object sliding once it's sliding than it is to start the object sliding in the first place), there are to coefficient of friction: one for static friction(μs) and one for kinetic friction(μk). For a given pair of surfaces, its virtually always true that  μk < μs . The magnitude of these two types of friction forces are given by the following equations:




           Fstatic friction, max = μsFN

                  Fkinetic friction = μkFN

Notice that the equation for the magnitude of the static friction force is for the maximum value. This is because static friction can vary, counteracting weaker forces that are less than the minimum force required to move an object. For example, suppose an object feels a normal force of F=100N, and the coefficient of static friction between it and the surface it's on is 0.5 then, the maximum force that static friction  can exert is (0.5)(100N) = 50N. However, if you push on the object with a force of, say 20N, then the static friction force will be 20N( in the opposite direction), not 50N: The object won't move. The net force on a stationary object must be zero. static friction can take on all values, up to a certain maximum, and you must overcome the maximum static friction force to get the object ti slide. The direction of Fkinetic friction  = Ff (kinetic) is opposite to that of motion (sliding), and the direction of Fstatic friction = Ff (static) is opposite to that of the intended motion.