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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