Classical Mechanics Lecture 6 Today’s Concept: Friction Mechanics Lecture 6, Slide 1

Classical Mechanics Lecture 6

Today’s Concept:Friction

Mechanics Lecture 6, Slide 1

Midterm Redux

Mechanics Lecture 6, Slide 2

Average=18.6/20

Seems like time is a big issue!!!Practice makes faster…

Friction

Mechanics Lecture 6, Slide 3

Friction

Mechanics Lecture 6, Slide 4

Friction

Mechanics Lecture 6, Slide 5

Friction

Always opposes the relative motion of two surfacesMechanics 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

Friction

Mechanics Lecture 6, Slide 13

Friction

Mechanics Lecture 6, Slide 14

Friction

Mechanics Lecture 6, Slide 15

Friction

Mechanics Lecture 6, Slide 16

Friction

Mechanics Lecture 6, Slide 17

Friction

Mechanics Lecture 6, Slide 18

Mechanics Lecture 6, Slide 19

Main Points

Mechanics Lecture 6, Slide 20

Main Points

Mechanics Lecture 6, Slide 21

Pre-lecture thoughts

Mechanics Lecture 6, Slide 22

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.phphttp://astro1.panet.utoledo.edu/~vkarpov/Static_Friction_nature.pdf

Mechanics Lecture 6, Slide 23

Mechanics Lecture 6, Slide 24

Mechanics Lecture 6, Slide 25

Mechanics Lecture 6, Slide 26

Mechanics Lecture 6, Slide 27

Mechanics Lecture 6, Slide 28

Mechanics Lecture 6, Slide 29

Mechanics Lecture 6, Slide 30

Mechanics Lecture 6, Slide 31

CheckpointA. B. C.

Mechanics Lecture 6, Slide 32

40%

13%

47%

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 33

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 34

M

f T

Clicker QuestionA. B. C. D.

Mechanics Lecture 6, Slide 35

0% 0%

100%

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

Mechanics Lecture 6, Slide 36

gmf k 11

gmf k 12

m

FamaF

47% got this right on first try

Checkpoint A. B. C.

Mechanics Lecture 6, Slide 37

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

Mechanics Lecture 6, Slide 38

00 nettotal FFa

38% got this right on first try

Checkpoint A. B. C.

Mechanics Lecture 6, Slide 39

0% 0%0%

0sin mgfFnet

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

65% got this right on first try

Mechanics Lecture 6, Slide 40

Case 2(With Friction)

Case 1(No Friction)

m2

m1

g

m2

m1

g

Resume here

Mechanics Lecture 6, Slide 42

Lets work it out

Mechanics Lecture 6, Slide 43

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 k. What is the tension in the string?

Tension in String

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 k. What is the tension in the string?

What is the relationship between the magnitude of the tension of the string at block 2 and the magnitude of the tension in the string at block 1?

A) T1 > T2 B) T1 = T2 C) T1 < T2

Mechanics Lecture 6, Slide 44

T1

T2m2

m1

g

Acceleration of coupled blocks

What is the relationship between the magnitudes of the acceleration of the two blocks?

A) a1 = a2 B) a1 < a2 C) a1 > a2

Mechanics Lecture 6, Slide 45

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 k. What is the tension in the string?

Mechanics Lecture 6, Slide 46

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

1) FBD

1) FBD2) F=ma

add

N = m2g

T – m2g = m2a m1g – T = m1a

m1g – m2g = m1a + m2a

a = m1g – m2g m1 + m2

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

Mechanics Lecture 6, Slide 47

T is smaller when a is bigger

m1g – T = m1a

T = m1g – m1aa = m1g – m2g m1 + m2

m2

m2g

T

N

f

m1

m1g

T

m2

m1

g

Mechanics Lecture 6, Slide 48

1) FBD2) F=ma

Mechanics Lecture 6, Slide 49

Accelerating Blocks

21 mm

T

m

Fa

amf 1

Mechanics Lecture 6, Slide 50

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 51

fRRv 2

maFN

RfR

va

22

2

Carnival Ride

Mechanics Lecture 6, Slide 52

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 53

Accelerating Truck

t

va

maFf

ga

mamgNf

S

SS

max

maxmax

Mechanics Lecture 6, Slide 54

Accelerating Truck

gm

mg

m

fa

mgNf

KKsliding

sliding

KKsliding

ga

mamgNf

S

SS

max

maxmax

Mechanics Lecture 6, Slide 55

Mass on Incline

sin

sin

gm

Fa

mgF

x

x

cossin

cos

kx

k

gm

fFa

mgf

Mechanics Lecture 6, Slide 56

Mass on Incline

x

mgk

m

xkg

m

xkfFa

mgf

s

sx

s

cossin

cossin)(

0

cos

Mechanics Lecture 6, Slide 57

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 58

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 59

Mass on Incline 2

cos

sin

cossin)(

0

cos

gmxk

g

m

xkg

m

xkfFa

mgf

s

sx

s

Mechanics Lecture 6, Slide 60

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 61

)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

Block

Mechanics Lecture 5, Slide 62

2

22

2sinsin

sin

2

2

1

t

xgmmamgf

m

fmg

m

Fa

t

xaatx

k

knet

Pushing Blocks

Mechanics Lecture 5, Slide 63

21

2

1223

22323

14323

1

1

1114323

1

1

4321

1

22

2)(

24

22)(

4)(

gmF

FFF

gmgmmNF

F

m

FmamammF

m

F

mmmm

Fa

hnetnetnet

net

hhnet

hh

yx

y

x

netF23