Friction Chapter Opener. Caption: Newton’s laws are fundamental in physics. These photos show two situations of using Newton’s laws which involve some new elements in addition to those discussed in the previous Chapter. The downhill skier illustrates friction on an incline, although at this moment she is not touching the snow, and so is retarded only by air resistance which is a velocity-dependent force (an optional topic in this Chapter). The people on the rotating amusement park ride below illustrate the dynamics of circular motion.

Consider An Object Coming to Rest Aristotle’s Idea: At rest is the “natural state” of terrestrial objects

Consider An Object Coming to Rest Aristotle’s Idea: At rest is the “natural state” of terrestrial objects Newton’s View: (Galileo’s too!) A moving object comes to rest because a force acts on it.

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

There are 2 types friction: Static (no motion) friction Friction is always present when 2 solid surfaces slide along each other. See 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

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.

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

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

Problems Involving Friction Set up the problem as usual, including the force of friction. For example, the hockey puck in the figure: Newton’s 2nd Law for the Puck:

Problems Involving Friction Set up the problem as usual, including the force of friction. For example, the hockey puck in the figure: Newton’s 2nd Law for the Puck: (In the horizontal (x) direction): ΣF = Ffr = -μkN = ma (1) (In the vertical (y) direction): ΣF = N – mg = 0 (2)

Problems Involving Friction Set up the problem as usual, including the force of friction. For example, the hockey puck in the figure: Newton’s 2nd Law for the Puck: (In the horizontal (x) direction): ΣF = Ffr = -μkN = ma (1) (In the vertical (y) direction): ΣF = N – mg = 0 (2) Combining (1) & (2) gives -μkmg = ma so a = -μkg

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

Static Friction Static Friction In many situations, the 2 surfaces are not slipping (moving) with respect to each other. This situation involves Static Friction The amount of the pushing force Fpush can vary without the object moving. The static friction force Ffr 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.

(In the horizontal (x) direction): Static Friction The static friction force Ffr 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 Fpush in the figure. Newton’s 2nd Law: (In the horizontal (x) direction): ∑F = Fpush - Ffr = ma = 0

(In the horizontal (x) direction): Static Friction The static friction force Ffr 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 Fpush in the figure. Newton’s 2nd Law: (In the horizontal (x) direction): ∑F = Fpush - Ffr = ma = 0 so Ffr = Fpush

(In the horizontal (x) direction): Static Friction The static friction force Ffr 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 Fpush in the figure. Newton’s 2nd Law: (In the horizontal (x) direction): ∑F = Fpush - Ffr = ma = 0 so Ffr = Fpush 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 Ffr.

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

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

Coefficients of Friction μs > μk Ffr (max, static) > Ffr (kinetic)

Conceptual Example A hockey puck is moving at a constant speed 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 Ffriction = μk N The force of Static Friction varies: Ffriction ≤ μs N For a given combination of surfaces, generally μs > μk 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 Fon ground . If the shoes do not slip, the force is due to static friction The shoes do not move relative to the ground

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

This is the force that propels Friction & Rolling The car’s tire does not slip. So, there is a friction force Fon ground between the tire & road. There is also a Newton’s 3rd Law reaction force Fon tire 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? Figure 5-4. Answer: Friction, of course! The normal force points out from the wall, and the frictional force points up.