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 phenomenoncalled 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) frictionKinetic (motion) friction

• Two types of friction:Static (no motion) frictionKinetic (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 ofAre the surfaces smooth or rough?

Are they wet or dry?Etc., etc., etc.

• Kinetic Friction is the same asSliding 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 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

• 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 later). Further,

k is dimensionlessUsually, k < 1

Problems Involving Friction

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

• 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 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.

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 = 0so 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.

• 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

The 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 (shown later). Further,

s is dimensionlessUsually, s < 1Always, k < s

Coefficients of Friction

μs > μk Ffr (max, static) > Ffr (kinetic)

Conceptual ExampleMoving 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 justFfriction = μk N

• The force of Static Friction varies by 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 groundThis 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 forcebetween the tire & road.

Friction & Rolling

• There is also a Newton’s 3rd Law reaction force on the tire.

This is the force that propels

the car forward

Example: Friction; Static & KineticA 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 ExampleYou 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?

m1: ∑F = m1a; x: FA – F21 – Ffr1 = m1ay: FN1 – m1g = 0

m2: ∑F = m1a; x: F12 – Ffr2 = m2ay: FN2 – m2g = 0

Friction: Ffr1 = μkFN1; Ffr2 = μkFN2

3rd Law: F21 = - F12

a = 1.88 m/s2

F12 = 368.5 N

FA =

m1 = 75 kgm2 = 110 kg

a FN1

FN2

Ffr1 Ffr2

m1g m2g

F21

F12