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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