Friction

Consider An Object Coming to Rest Aristotle’s idea: Rest is the “natural state” of terrestrial objects Newton’s view: A moving object comes to rest because a force acts on it. Most often, this stopping force is Due to a phenomenon called friction.

Friction Friction is always present when 2 solid surfaces slide along each other. See the figure. It must be accounted for when doing realistic calculations! It exists between any 2 sliding surfaces. There are 2 types friction: Static (no motion) friction Kinetic (motion) friction

Two types of friction: Static (no motion) friction Kinetic (motion) friction The size of the friction force depends on the microscopic details of the 2 sliding surfaces. These details aren’t fully understood & depend on the materials they are made of Are the surfaces smooth or rough? Are they wet or dry? Etc., etc., etc.

Kinetic Friction is the same as Sliding Friction. The kinetic friction force F fr opposes the motion of a mass. Experiments find the relation used to calculate F fr. F fr is proportional to the magnitude of the normal force N between 2 sliding surfaces. The DIRECTIONS of F fr & N are  each other!! F fr  N We write their relation as F fr   k F N (magnitudes)  k  Coefficient of Kinetic Friction

The Kinetic Coefficient of Friction  k Depends on the surfaces & their conditions. Is different for each pair of sliding surfaces. Values for μ k for various materials can be looked up in a table (shown later). Further,  k is dimensionless Usually,  k < 1

Problems Involving Friction Newton’s 2 nd Law for the Puck: (In the horizontal (x) direction): ΣF = F fr = -μ k N = ma (1) (In the vertical (y) direction): ΣF = N – mg = 0 (2) Combining (1) & (2) gives -μ k mg = ma so a = -μ k g Once a is known, we can do kinematics, etc. Values for coefficients of friction μ k for various materials can be looked up in a table (shown later). These values depend on the smoothness of the surfaces Set up the problem as usual, including the force of friction. For example, the hockey puck in the figure:

Static Friction In many situations, the two surfaces are not slipping (moving) with respect to each other. This situation involves Static Friction The amount of the pushing force F push can vary without the object moving. The static friction force F fr is as big as it needs to be to prevent slipping, up to a maximum value. Usually it is easier to keep an object sliding than it is to get it started.

Static Friction The static friction force F fr is as big as it needs to be to prevent slipping, up to a maximum value. Usually it is easier to keep an object sliding than it is to get it started. Consider F push in the figure. Newton’s 2 nd Law: (In the horizontal (x) direction): ∑F = F push - F fr = ma = 0 so F fr = F push This remains true until a large enough pushing force is applied that the object starts moving. That is, there is a maximum static friction force F fr.

Experiments find that the maximum static friction force F fr (max) is proportional to the magnitude (size) of the normal force N between the 2 surfaces. The DIRECTIONS of F fr & N are  each other!! F fr  N Write the relation as F fr (max) =  s N (magnitudes)  s  Coefficient of Static Friction Always find  s >  k  Static friction force: F fr   s N

The Static Coefficient of Friction  s Depends on the surfaces & their conditions. Is different for each pair of sliding surfaces. Values for μ s for various materials can be looked up in a table (shown later). Further,  s is dimensionless Usually,  s < 1 Always,  k <  s

Coefficients of Friction μ s > μ k  F fr (max, static) > F fr (kinetic)

Conceptual Example Moving at constant v, with NO friction, which free body diagram is correct?

Static & Kinetic Friction

Kinetic Friction Compared to Static Friction Consider both the kinetic and static friction cases –Use the different coefficients of friction The force of Kinetic Friction is just F friction = μ k N The force of Static Friction varies by F friction ≤ μ s N For a given combination of surfaces, generally μ s > μ k It is more difficult to start something moving than it is to keep it moving once started

Friction & Walking The person “pushes” off during each step. The bottoms of his shoes exert a force on the ground This is If the shoes do not slip, the force is due to static friction –The shoes do not move relative to the ground

Newton’s Third Law tells us there is a reaction force This force propels the person as he moves If the surface was so slippery that there was no frictional force, the person would slip

The car’s tire does not slip. So, there is a frictional force between the tire & road. Friction & Rolling There is also a Newton’s 3 rd Law reaction force on the tire. This is the force that propels the car forward

Example: Friction; Static & Kinetic A box, mass m =10.0-kg rests on a horizontal floor. The coefficient of static friction is  s = 0.4; the coefficient of kinetic friction is  k = 0.3. Calculate the friction force on the box for a horizontal external applied force of magnitude: (a) 0, (b) 10 N, (c) 20 N, (d) 38 N, (e) 40 N.

Conceptual Example You can hold a box against a rough wall & prevent it from slipping down by pressing hard horizontally. How does the application of a horizontal force keep an object from moving vertically?

m 1 : ∑F = m 1 a; x: F A – F 21 – F fr1 = m 1 a y: F N1 – m 1 g = 0 m 2 : ∑F = m 1 a; x: F 12 – F fr2 = m 2 a y: F N2 – m 2 g = 0 Friction: F fr1 = μ k F N1 ; F fr2 = μ k F N2 3 rd Law: F 21 = - F 12 a = 1.88 m/s 2 F 12 = N F A = m 1 = 75 kg m 2 = 110 kg a F N1 F N2 F fr1 F fr2 m1gm1g m2gm2g F 21 F 12