Physics 2211: Lecture 11 Todays Agenda

1
Physics 2211 Lecture 11Todays Agenda

• Friction
• What is it?
• How do we characterize it?
• Model of friction
• Static Kinetic friction
• Some problems involving friction

2
New Topic Friction

• What does it do?
• It opposes motion!
• How do we characterize this in terms we have
  learned?
• Friction results in a force in the direction
  opposite to the direction of motion!

y
x
3
Friction...

• Friction is caused by the microscopic
  interactions between the two surfaces

• Friction force is the result of the
  electromagnetic forces acting between the two
  surfaces.

4
Friction...

• Force of friction acts to oppose motion
• Parallel to surface.
• Perpendicular to Normal force.

y
x
5
Model for Sliding Friction

• The direction of the frictional force vector is
  perpendicular
• to the normal force vector .

• The constant ?K is called the coefficient of
  kinetic friction.

6
Model...

• Dynamics
• SFX FA ? ?KN ma
• SFY N mg
• so FA ???Kmg ma

y
Assume forces are acting at center of mass of
block.
x
7
Example Forces and Motion

• A box of mass m1 1.5 kg is being pulled by a
  horizontal string having tension T 90 N. It
  slides with friction (mk1 0.51) on top of a
  second box having mass m2 3 kg, which in turn
  slides with friction (mk2 0.068) on a floor.
• What is the acceleration of the second box (m2) ?

slides with friction (mk10.51 )
T
m1

slides with friction
(mk20.068 )
a ?
m2
8
Example Forces and Motion

• First draw FBD of the top box

N1
m1
fK1 - mK1N1
T
y
- m1g
x
9
Example Forces and Motion

• Newtons 3rd law says the forces on box 1 exerted
  by box 2 are equal and opposite to the forces on
  box 2 exerts by box 1.

• As we just saw, these forces are due to friction
  and the normal force.

N1 m1g
- mK1m1g
m1
fK1
m2
- fK1
- N1
10
Example Forces and Motion

• Now consider the FBD of box 2

N2
fK1 mk1m1g
m2
fK2 mk2N2
-N1 -m1g
-m2g
11
Inclined Plane with Friction

• Draw free-body diagram

a
y
?
x
12
Inclined plane...

• Resolve force due to gravity into components.

• Applied Newtons 2nd law in both dimensions.

y
x
13
Static Friction...

• So far we have considered friction acting when
  something moves.
• We also know that it acts in un-moving static
  systems
• In these cases, the force provided by friction
  will depend on the forces applied on the system.

y
x
14
Static Friction...

• Just like in the sliding case except a 0.
• x FA ??fF 0
• y N mg

• While the block is static fF ??FA

y
x
15
Static Friction...

• The maximum possible force that the friction
  between two objects can provide is fMAX ?SN,
  where ?s is the coefficient of static friction.
• So fF ? ?S N.
• As one increases F, fF gets bigger until fF ?SN
  and the object starts to move.

y
x
16
Static Friction...

• ?S is discovered by increasing F until just
  before the block starts to slide
• x FMAX ?? fMAX 0 but fMAX ?SN
• y N mg
• ?S ??FMAX / mg

y
x
17
Example Forces and Motion

• A box of mass m 10.21 kg is at rest on a floor.
  The coefficient of static friction between the
  floor and the box is ms 0.4.
• A rope is attached to the box and pulled at an
  angle of q 30o above horizontal with tension T
  40 N.
• Does the box move?

T

q
m
static friction (ms 0.4 )
18
Example Forces and Motion

• Pick axes draw FBD of box.

y N T sin q - mg maY 0
N mg - T sin q
x T cos q - fF maX
m
The box will move if T cos q - fF gt 0
19
Static Friction

• We can also consider ?S on an inclined plane.
• In this case, the force provided by friction will
  depend on the angle ? of the plane.

?
20
Static Friction...

• The force provided by friction, fF , depends on ?.

fF
N
a 0 (block is not moving)
mg sin ????fF ???
?
(Newtons 2nd Law along x-axis)
mg
?
21
Static Friction...

• We can find ?s by increasing the ramp angle until
  the block slides

mg sin ?M ???fF????
fF
N
In this case
?fF????SN ? ??Smg cos ?M
mg sin ?M????Smg cos ?M????
?M
mg
?
?S???tan ?M?
22
Additional comments on Friction

• Since fF ?N , the force of friction does not
  depend on the area of the surfaces in contact.
• By definition, it must be true that ?S gt ?K
  for any system (think about it...).

23
Aside

• Graph of Frictional force vs Applied force

fF ?SN
fF ?KN
fF
fF FA
FA
24
Problem Box on Truck

• A box with mass m sits in the back of a truck.
  The coefficient of static friction between the
  box and the truck is ?S.
• What is the maximum acceleration a that the
  truck can have without the box slipping?

?S
m
a
25
Problem Box on Truck

• Draw Free Body Diagram for box
• Consider case where fF is max...(i.e. if the
  acceleration were any larger, the box would
  slip).

N
y
fF ?SN
x
mg
26
Problem Box on Truck

• Use for both x and y
  directions
• x ?SN maMAX
• y N mg
• aMAX ?S g

N
y
aMAX
fF ?SN
x
mg
27
Lecture 11, ActForces and Motion

• An inclined plane is accelerating with constant
  acceleration a. A box resting on the plane is
  held in place by static friction. What is the
  direction of the static frictional force?

?S
a
fF
fF
fF
(a) (b) (c)
28
Recap of todays lecture

• Friction
• What is it?
• How do we characterize it?
• Model of friction.
• Static Kinetic friction.
• Some problems involving friction.
• Read Sections 5.2 in Tipler.