Announcements

1

• Announcements
• Famous interdisciplinary physics colloquium this
  week
• Tolerance and Intolerance in Protein Structure
  and Function
• Review of Thursdays lecture introduction to
  Newtons laws
• Todays lecture
• More examples of the application of Newtons laws
• Friction forces

2
Newtons 2nd Law Example
T
T mg ma Tmgmamg(1a/g)
a
For example mg 500 N
a 4.9 m/s2 T ?
m
750 N
3
From HW 5
j
N
i
mg
4
j
T
N
f
i
mg
5
mg
T
T
mg
T
T
mg
mg
6
radial -T mg -mv2/r tangential 0 m aq
mg
T
tangential
radial
radial -T -mv2/r tangential mg m aq
T
mg
q
T
T
mg
radial Tmg cosq mv2/r tangential -mg sinq
m aq
radial T mg mv2/r tangential 0 m aq
mg
7
Newtons second law F m a
Types of forces Fundamental Approximate
Empirical Gravitational F-mg j
Friction Electrical Support
Magnetic Elastic Elementary
particles
8
Friction forces The term friction is used to
describe the category of forces that oppose
motion. One example is surface friction which
acts on two touching solid objects. Another
example is air friction. There are several
reasonable models to quantify these phenomena.
Surface friction
Normal force between surfaces
Material-dependent coefficient
Air friction
K and K are materials and shape dependent
constants
9
Models of surface friction forces
fs,maxmsn
surface friction force
(applied force)
Coefficients of friction ms , mk depend on the
surfaces usually, ms gt mk
10
Some estimates of static and kinetic friction
Material ms mk
Rubber on concrete 1.0 0.8
Wood on wood 0.3 0.2
Steel on steel with lubrication 0.09 0.05
Teflon on teflon 0.04 0.04
11
Surface friction
F-fs 0 if Fltmsnmsmg
if Fgtmsnmsmg , then F-fkma (fk mkmg)

12
N
v0
f mkN
mg
13
j
T
N
q
f
X
i
mg
f ? a ?
14
n
f
mg cos q
mg
mg sin q
q
just before block slips fs,max-mg sin q ms
n-mg sin q ms mg cosq -mg sinq 0
? ms tan q
15
(No Transcript)
16
Peer instruction question
f
q
Suppose that ms0.75 which means that the block
starts to slide when q 37o. What is f when q
20o? (a) mg sinq (b) ms mg sinq (c)mg cosq
(d) ms mg cosq
17
Peer instruction question
f
q
Suppose that ms0.75 which means that the block
starts to slide when q 37o. What is f when q
40o? (a) mg sinq (b) mk mg sinq (c)mg cosq
(d) mk mg cosq
18
radial -fs -m v2/r extreme condition
fs,maxms n ms mg ? vmax
19
fs
Banked curve (ignoring friction) Optimal
banking angle
20
More practice with Newtons laws
n
F
fs
mg
q
along surface F-mg sinq fs 0 perpendicular
to surface n mg cosq 0 ? n mg cosq
Condition for pushing up the incline F gt mg
(sinqms cosq )
21
More practice with Newtons laws
F
n
fs
mg
q
along surface F cosq -mg sinq fs
0 perpendicular to surface n Fsinq- mg cosq
0 Condition for pushing up the incline
22

• Peer instruction question
• Suppose that the forces on a soap bubble falling
  through the air can be described by
  If at t0 v(t)0, what will be its
  velocity at a later time?
• v(t)gt (The bubble will accelerate under the
  effects of gravity and air friction (the b
  term) has a negligible effect.)
• v(t)0 (Air friction will eventually stop the
  bubble from moving.)
• v(t)(Constant) (The magnitude of the air
  friction force will increase with time,
  eventually balancing the force of gravity.)
• v(t)gtgt (Air friction makes the bubble move
  faster than gravity alone.

23
Examples (one dimension)
(constant)