N
e
w
t
o
n
s
T
h
i
r
d
L
a
w
P
a
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t
2
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Newtons 3rd Law
Last Time :
How to deal with more than one object!
A
r
FBonA
B
r
nA
r
r
FAonB = FBonA
r
FAonB
r
nB
r
FBonA
r
FAonB
r
F(G ) A
2nd Law
r
Fnet = mA a
r
F(G ) B
r 2nd Law
Fnet = mB
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Getting Help
The Physics Learning Center
GTA Office Hours
Supplemental Instruction:
Every Wednesday Starting Next Wednesday January 26th
7 8:30 PM Fisher Hall Room 130
Get Help with
Assigned Chapter Problems
MasteringPhysics Prob
Kinematics in Two Dimensions
Kinematics
Part 2
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Uniform Circular Motion
Last time :
Angular Position
Angular velocity
Tangential Speed
s
(radians)
r
d
= lim
=
t 0 t
dt
vt
r`
[]
ra
s
ds d ( r )
d
vt =
=
=r
= r
dt
dt
dt
Kinematic Equa
Exam I
February 1st
6:00 7:30 PM
All conflicts must be resolved by
January 28th 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
Exam I Feb 1
Exam
st
6
Last Lecture .
Kinematics - the Description of motion
Some Simplifications :
Assume motion is along a straight line.
Linear Motion
Assume that objects are treated as
geometric points. Particle Model
Graphical Description of Motion with Diagrams
Graphical
Kinematics in Two Dimensions
Kinematics
Part 1
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Two-Dimensional Motion
Two-Dimensional
Ski Jumping
09/12/13
2
Ski Jumping Motion Diagram
Ski
Start
r
vi
r
v
r
vf
r
vi
r
vf
r
v
r
vi
r
a
r
a
r
vi
r
vf
r
vf
Acceleration is the same everywhe
Welcome to PH2100!
Welcome
Introductory Classical Mechanics
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Introductions
Introductions
Lecturer (section 0B)
Dr. Brian Fick
All PH2100 Questions
Wil Slough
213 Fisher
wjslough@mtu.edu
09/12/13
2
What Materials are Required?
What
The T
Newtonian Gravity II
Physics 2100
(2011)
MTU
Reminder
Thursday
9/12/13
: MasteringPhysics HW # 14
2
Newtons Law of Gravity
r
m1
r
F2 on 1
F1 on 2
r
F1 on 2
m2
Gm1m2
= F2 on 1 =
r2
The forces are directed along the straight line joining the two objects.
9/
Newtons Theory
Of Gravity
Learning Objectives
To
understand the historical
significance of the Newtonian
synthesis
To
study the dynamics associated
with a distance-dependent force
To
understand satellite and planetary
motion
9/12/13
2
The Newtonian Synthe
Last Time :
For Conservative forces
Conservation of
Mechanical Energy
For Non-Conservative forces
like Friction
Mechanical Energy is
Dissipated (as Heat)
cfw_Wnc = Eth
Emech = 0
K f + U f = Ki + U i
Emech = Wnc
K f K i + U f U i = Wnc
Presently, we canno
Work/EnergyTransfer
Revisited
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System Energy Esys = K + U + Eth
Mechanical Energy
K = 1 mv 2
2
Emech = K + U
U = mgy
Due to: vertical
position y in
gravitational field
and/or
U = 1 k (s ) 2
2
Due to: Spring
displacement s
Kinetic Energy
W o rkP a rt2
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Exam III Scores (Avg = 115.8 pts, 77.2 %)
12
10
6
4
2
0
Score
Frequency
8
F o rc e s c h a ng e a no b je c ts kine tic e ne rg y b yd o ing
wo rk.
Object moving from point si to sf
in the presence of a constant
force F.
Work Part 1
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Learning Objectives
Learning
To
define work
To
use the work-kinetic energy
theorem to solve energy-related
problems
09/12/13
2
Work
What is the relationship between Kinetic Energy
and Force ?
r
Initial Kinetic F
Final Kinet
Some Energy Exercises
Energy Problems :
What are the concepts we have to work with?
Mechanical Energy
K = 1 mv 2
2
Gravitational potential
energy
Spring
energy
( E la
ene stic po
rgy
te n
)
t ia l
Ch. 10
E = K +Ug +Us
Kinetic energy
U g = mgy
U s = 1 k (
Exam III
April 5th 6:00 7:30 PM
All conflicts must be resolved by
April 1st 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
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Exam II
Exam III
April 5th 6:00 7:30 PM
All conflicts must be resolved by
April 1st 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
Energy Part 2
Energy
cfw_ P
Impulse-Momentum Theorem
Impulse-Momentum
Momentum:
( in x-direction )
px = mv x
Impulse-momentum theorem:
An impulse delivered to a particle
changes the particles momentum.
09/12/13
Impulse:
( in x-direction )
tf
J x = Fx (t )dt
ti
J x = p x
pfx = pix +
Impulse and Momentum
Part 1
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The Fundamental Questions
The
How
do we describe motion?
Kinematics
What are the causes of changes in motion?
Dynamics
What properties of a system of particles do
not change as the particles interact?
Conser
Exam II
March 1st
6:00 7:30 PM
All conflicts must be resolved by
February 25th 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
Exam II March 1st 6 to 7
Exam II
March 1st
6:00 7:30 PM
All conflicts must be resolved by
February 25th 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
Exam II March 1st 6 to 7
Exam II
March 1st
6:00 7:30 PM
All conflicts must be resolved by
February 25th 5PM
E-mail wjslough@mtu.edu
with a detailed description of the nature
of your conflict (class, time) if you need
to take this exam at a different time.
More On
Newtons
Laws of
N
e
w
t
o
n
s
3
r
d
P
a
r
t
3
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Reminder
Exam II
On the Horizon
st
March 1
(Chapters 5 - 8.3)
09/12/13
2
mass of A > mass of B
A
A
09/12/13
B
B
3
PQ1: While student B pushes away from student
A, their contact force forms an action/reacti
N
e
w
t
o
n
s
T
h
i
r
d
L
a
w
P
a
r
t
2
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Learning Objectives
Learning
To understand tension forces
To use an expanded problemsolving strategy for dynamics
problems
09/12/13
2
PQ0: I am taking, or took PH1100
(Physics Lab I)
(A)
(B)
(C
Stranger Than Friction?
Pull
Pull = 0
Pull
Pull = 0
Pull 0
Pull Pull
=
PullPull 0
Pull =
=0
Pull
Pull = 0
fs = 0
fs
k
fPull 0
s
Pull= 0
f=
k
s
Pull f
Pull = 0s = 0
f
k
s
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fs = 0
fs
k
fs = 0
fffs = 0
ss = 0
k
fsfs
kk
fs = 0
fs
k
A little
Stranger Than Friction?
Pull
Pull = 0
Pull
Pull = 0
Pull 0
Pull Pull
=
PullPull 0
Pull =
=0
Pull
Pull = 0
fs = 0
fs
k
fPull 0
s
Pull= 0
f=
k
s
Pull f
Pull = 0s = 0
f
k
s
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fs = 0
fs
k
fs = 0
fffs = 0
ss = 0
k
fsfs
kk
fs = 0
fs
k
A little
Dynamics I Motion Along a Line
Part 2
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Learning Objectives
Learning
To review and solidify a few things about
dynamics.
To introduce a simple model for friction
To introduce a simple model for drag
force.
To continue to use Newtons
Dynamics I: Motion Along a Line
Part 1
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Frequency
Exam I Scores (Avg = 122.3 out of 150 pts, 81.6 %)
Score
Learning Objectives
Learning
To learn to use free-body diagrams
To understand the distinction between
mass and the gravitationa
Dynamics I: Motion Along a Line
Part 1
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Frequency
Exam I Scores (Avg = 122.3 out of 150 pts, 81.6 %)
Score
Learning Objectives
Learning
To learn to use free-body diagrams
To understand the distinction between
mass and the gravitationa