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


Average=18.6/20

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

Friction


Friction


Friction


Friction

Always opposes the relative motion of two surfacesMechanics Lecture 6, Slide 6

Friction


Static Friction


Static Friction


Static Friction


Without Friction


sin

sing

m

mg

m

Fa net

Friction


Friction


Friction


Friction


Friction


Friction


Friction



Main Points


Main Points


Pre-lecture thoughts


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


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









CheckpointA. B. C.


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.


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


M

f T

Clicker QuestionA. B. C. D.


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


gmf k 11

gmf k 12

m

FamaF

47% got this right on first try

Checkpoint A. B. C.


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


00 nettotal FFa


Checkpoint A. B. C.


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



Case 2(With Friction)

Case 1(No Friction)

m2

m1

g

m2

m1

g

Resume here


Lets work it out


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


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


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


m2

m1

g



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


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


1) FBD2) F=ma


Accelerating Blocks

21 mm

T

m

Fa

amf 1


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


fRRv 2

maFN

RfR

va

22

2

Carnival Ride


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


Accelerating Truck

t

va

maFf

ga

mamgNf

S

SS

max

maxmax


Accelerating Truck

gm

mg

m

fa

mgNf

KKsliding

sliding

KKsliding

ga

mamgNf

S

SS

max

maxmax


Mass on Incline

sin

sin

gm

Fa

mgF

x

x

cossin

cos

kx

k

gm

fFa

mgf


Mass on Incline

x

mgk

m

xkg

m

xkfFa

mgf

s

sx

s

cossin

cossin)(

0

cos


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


Mass on Incline 2

sin

sin

gm

Fa

mgF

x

x

cos

sin

cossin

cos

g

ag

gm

fFa

mgf

k

kx

k


Mass on Incline 2

cos

sin

cossin)(

0

cos

gmxk

g

m

xkg

m

xkfFa

mgf

s

sx

s


Mass on Incline 2

sincos

)cos(sin

sincos

cossin

)sincos(cossin

0

)sincos(

s

s

s

s

s

ss

mgmgmgT

TmgTmg

a

TmgNf


)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


2

22

2sinsin

sin

2

2

1

t

xgmmamgf

m

fmg

m

Fa

t

xaatx

k

knet

Pushing Blocks


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

Documents

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