Unit 6 Friction

Mechanics Lecture 6, Slide 1

Today’s Concept:Friction UP

Midterm 1

Mechanics Lecture 6, Slide 2

Average=102.1”%”

Excellent Job!You can do the problems!

Unit 5 Homework

Mechanics Lecture 6, Slide 3

Deadline for unit 5 Extended until this Thursday @ 11:30 Pm

Two of the problems were for unit 6….

Video Prelectures/lecture Thoughts

Mechanics Lecture 6, Slide 4

Friction

Mechanics Lecture 6, Slide 5

Friction

Always opposes the relative motion of two surfaces

Mechanics Lecture 6, Slide 6

Friction

Mechanics Lecture 6, Slide 7

Static Friction

Mechanics Lecture 6, Slide 8

Static Friction

Mechanics Lecture 6, Slide 9

Static Friction

Mechanics Lecture 6, Slide 10

Without Friction

Mechanics Lecture 6, Slide 11

sin

sing

m

mg

m

Fa net

Friction

Mechanics Lecture 6, Slide 12

xx maF yy maF

Note that we have rotated the coordinate system!!!

Friction

Mechanics Lecture 6, Slide 13

xx maF yy maF

Note that we have rotated the coordinate system!!!

0ˆ

ˆcosˆ

jma

jmgjNF

y

y

cosmgN

Friction

Mechanics Lecture 6, Slide 14

xx maF

Note that we have rotated the coordinate system!!!

imaifimgF xkxˆˆˆsin

cosmgN

Nf kk cosmgk

cossin gmmgma kx

cossin kx ga

Block

Mechanics Lecture 5, Slide 15

22 2

2

1

t

xaatx

m

fmg

m

Fa knet

sin

2

2sinsin

t

xgmmamgfk

Static Friction

Mechanics Lecture 6, Slide 16

xx maF ifimgF sxˆˆsin

cosmax, mgNf sss

cossin mgmg s

maxmax cossin mgmg s

Starts to Slide

maxmax cossin s

maxmax

max tancos

sin s

Static Friction/Car Skidding

Mechanics Lecture 6, Slide 17

Pushing Blocks

Mechanics Lecture 5, Slide 18

Pushing Blocks

Mechanics Lecture 5, Slide 19

netF23

gmgmmNFynet 14323 2)(

1

1

4321

1

4)( m

F

mmmm

Fa hh

24

22)( 1

1

1114323

hhnet

F

m

FmamammF

x

21

2

1223

22323 2

2gm

FFFF h

netnetnet yx

xnetF23

Force to accelerate twoBlocks with acceleration=a

ynetF23

Normal force = weight of two blocks

Main Points

Mechanics Lecture 6, Slide 20

Main Points

Mechanics Lecture 6, Slide 21

CheckPoint

A block slides on a table pulled by a string attached to a hanging weight. In Case 1 the block slides without friction and in Case 2 there is kinetic friction between the sliding block and the table.

In which case is the tension in the string biggest?A) Case 1 B) Case 2 C) Same

68% got this right on first try

Mechanics Lecture 6, Slide 22

Case 2(With Friction)

Case 1(No Friction)

m2

m1

g

m2

m1

g

In which case is the tension in the string biggest?A) Case 1 B) Case 2 C) Same

B) M1 will not be accelerating as fast in case two than in case one because there is the extra force of friction acting against mass 1. Since the acceleration is smaller in case two, there has to be more of a force acting against gravity, the only other possible force is Tension.

Mechanics Lecture 6, Slide 23

Case 2(With Friction)

Case 1(No Friction)

m2

m1

g

m2

m1

g

Lets work it out

Mechanics Lecture 6, Slide 24

m2

m1

g

A block (m2) slides on a table pulled by a string attached to a mass (m1) hanging over the side. The coefficient of kinetic friction between the sliding block and the table is mk. What is the tension in the string?

Mechanics Lecture 6, Slide 27

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

1) FBD

1) FBD2) SF=ma

add

N = m2g

T – m m2g = m2a m1g – T = m1a

m1g – m m2g = m1a + m2a

a = m1g – m m2g m1 + m2

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

Mechanics Lecture 6, Slide 28

T is smaller when a is bigger

m1g – T = m1a

T = m1g – m1aa = m1g – m m2g m1 + m2

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

Mechanics Lecture 6, Slide 29

1) FBD2) SF=ma

CheckpointA. B. C.

Mechanics Lecture 6, Slide 30

0% 0%0%

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.

If the truck moves with constant acceleration to the left as shown, which of the following diagrams best describes the static frictional force acting on the box:

Sa

A B C

CheckPoint

If the truck moves with constant accelerating to the left as shown, which of the following diagrams best describes the static frictional force acting on the box:

A B C

A) In order to keep the box from sliding to the back of the truck as it accelerates, the frictional force needs to pull/push the box forward.

B) Friction always opposes motion/acceleration.

Mechanics Lecture 6, Slide 31

Sa

56% correct

Clicker Question

A box of mass M sits on a horizontal table. A horizontal string having tension T applies a force on the box, but static friction between the box and the table keeps the box from moving.

What is the magnitude of the total force acting on the box?

Since acceleration is zero.

A) MgB) mMgC) TD) 0

Mechanics Lecture 6, Slide 32

M

f T

Clicker QuestionA. B. C. D.

Mechanics Lecture 6, Slide 33

0% 0%0%0%

A box of mass M sits on a horizontal table. A horizontal string having tension T applies a force on the box, but static friction between the box and the table keeps the box from moving.

What is the magnitude of the static frictional force acting on the box?

Since the box is not moving the forces must be equal, otherwise there would be an acceleration.

A) MgB) mMgC) TD) 0

M

f T

38% correct

Checkpoint A. B. C.

Mechanics Lecture 6, Slide 34

0% 0%0%

gm

f

m

Fa k

net 1

1

11

1

gm

f

m

Fa k

net 2

2

22

2

gaa k 21

28% got this right on first try

Mechanics Lecture 6, Slide 35

00 nettotal FFa

44% got this right on first try

Checkpoint A. B. C.

Mechanics Lecture 6, Slide 36

0% 0%0%

0sin mgfFnet

Mechanics Lecture 6, Slide 37

Mechanics Lecture 6, Slide 38

Mechanics Lecture 6, Slide 39

Mechanics Lecture 6, Slide 40

Mechanics Lecture 6, Slide 41

Mechanics Lecture 6, Slide 42

Mechanics Lecture 6, Slide 43

Mechanics Lecture 6, Slide 44

Microscopic explanation of Friction

What is Friction?Why can’t we walk through walls?

Basically the same answer to both questions…

Electron clouds of atoms repel (or bond to) each other

http://www.virneth.co.uk/topFriction/friction0.php http://astro1.panet.utoledo.edu/~vkarpov/Static_Friction_nature.pdf

Mechanics Lecture 6, Slide 45

Climbing Skins for Touring Skis

Mechanics Lecture 6, Slide 46

Mechanics Lecture 6, Slide 47

Accelerating Blocks

21 mm

T

m

Fa

amf 1

Mechanics Lecture 6, Slide 48

gmmT

gm

gm

m

fa

gmf

S

SS

S

)( 21max

2

2

2

2

22

max

max

Accelerating Blocks

gm

gm

m

fa

gmf

kk

k

2

2

2

2

22

21

2

mm

fT

m

Fa

Mechanics Lecture 6, Slide 49

fRRv 2

maFN

RfR

va

22

2

Carnival Ride

Mechanics Lecture 6, Slide 50

Rf

g

Rf

gR

v

gR

Rv

g

a

g

ma

mg

N

mg

mgNf

s

s

s

22

22

22

/

min

min

min

Carnival Ride

min

min

1

s

s

W

N

mgNf

Mechanics Lecture 6, Slide 51

Accelerating Truck

t

va

maFf

ga

mamgNf

S

SS

max

maxmax

Mechanics Lecture 6, Slide 52

Accelerating Truck

gm

mg

m

fa

mgNf

KKsliding

sliding

KKsliding

ga

mamgNf

S

SS

max

maxmax

Mechanics Lecture 6, Slide 53

Mass on Incline

sin

sin

gm

Fa

mgF

x

x

cossin

cos

kx

k

gm

fFa

mgf

Mechanics Lecture 6, Slide 54

Mass on Incline

x

mgk

m

xkg

m

xkfFa

mgf

s

sx

s

cossin

cossin)(

0

cos

Mechanics Lecture 6, Slide 55

cos

)cos)((sin

)(cos)(sin)(0

sin

sin

cos

cos

2

1212

2

22121

2

21

1

2

11

222

min

min12

1

2

min

m

mmm

m

mmgmmg

m

ffFFa

gmF

gmF

gmf

gmf

ss

ssxx

x

x

s

s

Mass on Incline

Mechanics Lecture 6, Slide 56

Mass on Incline 2

sin

sin

gm

Fa

mgF

x

x

cos

sin

cossin

cos

g

ag

gm

fFa

mgf

k

kx

k

Mechanics Lecture 6, Slide 57

Mass on Incline 2

cos

sin

cossin)(

0

cos

gm

xkg

m

xkg

m

xkfFa

mgf

s

sx

s

Mechanics Lecture 6, Slide 58

Mass on Incline 2

sincos

)cos(sin

sincos

cossin

)sincos(cossin

0

)sincos(

s

s

s

s

s

ss

mgmgmgT

TmgTmg

a

TmgNf

Mechanics Lecture 6, Slide 59

)cos(sin

)sincos(

)(cos)(sin

)(cos)(sin)(0

sin

sin

cos

cos

212

22121

2

22121

2

21

1

2

11

222

min

min12

1

2

min

s

s

ss

ssxx

x

x

s

s

mm

mmgmmg

m

mmgmmg

m

ffFFa

gmF

gmF

gmf

gmf

Mass on Incline 2