Outline:

Types of Friction

Dry Friction

Static vs. Kinetic

Angles

Applications of Friction

ENGR 1205 1 Appendix B

Contacting surfaces typically support

normal and tangential forces

Friction is a tangential force

Friction occurs whenever there is a

tendency for one surface to slide

along another

Friction opposes this tendency

ENGR 1205 Chapter 6 2

Friction occurs when any two objects are

in contact

Some case we try to minimize friction (to

minimize energy loss)

Bearings, fluid flow etc.

Some cases we try to maximize friction

Brakes

We rely on friction to walk

ENGR 1205 Chapter 6 3

Dry (Coulomb friction)

Friction force is tangential to surfaces of contact

Friction occurs before sliding and during sliding

Friction opposes direction of motion

Fluid

Adjacent layers of fluid (liquid or gas) move at different

velocities

Depends on velocity gradients and viscosity

Internal

Function of deformation and elasticity

ENGR 1205 Chapter 6 4

If the box is in static equilibrium, then P=F

As P increases, F increases, until force P

becomes high enough to overcome static friction.

Static friction must be determined from a free

body diagram because it depends on P.

Kinetic friction is constant for all values of P.

ENGR 1205 Chapter 6 5

Object is NOT sliding

Friction is determined by FBD and equations of

equilibrium

Maximum value of static friction is 𝑭𝒎𝒂𝒙 = 𝝁𝒔𝑵

When F = Fmax motion is IMPENDING

When 𝟎 < 𝑭𝒔 ≤ 𝝁𝒔𝑵 object is in equilibrium

ENGR 1205 Chapter 6 6

Object is slding and generally object is NOT in equilibrium (P>Fk)

Friction force is constant and determined by:

𝑭𝒎𝒂𝒙 = 𝝁𝒔𝑵

Object could in equilibrium (only happens if it is already moving

Generally, μk < μs ENGR 1205 Chapter 6 7

The resultant contact force is

R acting at an angle

When the friction is a maximum

(impending motion) then the

angle is also at a maximum

φ

N

F

N

Ftan

R

ENGR 1205 8 Appendix B

ssN

F maxtan

Ff = 0 for smooth surfaces

FN = normal force

Ff ≤ µsFN for no motion,

µs= coefficient of static friction

Ff = µsFN for impending motion

(about to slide)

Ff = µkFN for motion,

µk= coefficient of kinetic friction

Ff opposes direction of

(impending) motion

ENGR 1205 Appendix B 9

ENGR 1205 Appendix B 10

Sliding vs. Tipping Consider pushing (with force P)

on a uniform crate of weight W that sits on a rough surface. As P increases the crate will slip or tip. If the μs is large then the normal force with shift to the

corner 𝒙 =𝒃

𝟐 and the crate

will tip over. So, apply N at some unknown distance from the centre line and solve for x.

ENGR 1205 Chapter 6 11

Assume it is in equilibrium

not moving, acceleration = 0

Treat friction as an unknown & solve from FBD

If Fsolved > sN, then the friction required to

maintain static equilibrium is larger than the

maximum friction available

the object slides

ENGR 1205 12 Appendix B

A 100 N force acts as shown on a 300 N block

placed on an inclined plane. The coefficients

of friction between the block and the plane

are μs = 0.25 and μk = 0.20. Determine

whether the block is in equilibrium.

ENGR 1205 13 Appendix B

3

4

100 N

ENGR 1205 Appendix B 14

It is observed that when the bed of a dump

truck is raised to an angle of 25o the vending

machines begin to slide off the bed.

Determine the coefficient of static friction

between them and the surface of the truck.

ENGR 1205 15 Appendix B

0.3 m

0.3 m

0.5 m

G

25o

ENGR 1205 Appendix B 16

ENGR 1205 Appendix B 17

The coefficients of friction are s = 0.40 and

k = 0.30 between all surfaces of contact.

Determine the force P for which motion of the

30 kg block is impending if cable AB is

attached as shown.

ENGR 1205 18 Appendix B

ENGR 1205 Appendix B 19

ENGR 1205 Appendix B 20

ENGR 1205 Appendix B 21

The movable bracket

shown may be placed at

any height on the 0.076 m

diameter pipe. If the

coefficient of static

friction between the pipe

and the bracket is 0.25,

determine the minimum

distance x at which the

load W can be supported.

Neglect the weight of the

bracket.

ENGR 1205 22 Appendix B

0.15 m

0.076 m

ENGR 1205 Appendix B 23

ENGR 1205 Appendix B 24

ENGR 1205 Appendix B 25

Beam AB is subjected to a uniform load of

200 N/m and is supported at B by post BC.

Determine the minimum force P required to

pull the post out from under the beam if the

coefficients of static friction are B= 0.2

and C= 0.5. Neglect the weight of the

members and the thickness of the post.

ENGR 1205 26 Appendix B

4 m 0.75 m

0.25 m

A B

C

ENGR 1205 Appendix B 27

ENGR 1205 Appendix B 28