PHY 113 C Fall 2013 Lecture 17 1 PHY 113 C General Physics I 11 AM 1215 PM TR Olin 101 Plan for Lecture 17 Review of Chapters 913 1516 Comment on exam and advice for preparation ID: 136640
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PHY 113 C Fall 2013 -- Lecture 17
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PHY 113 C General Physics I
11 AM – 12:15 PM TR Olin 101
Plan for Lecture 17:
Review of Chapters 9-13, 15-16
Comment on exam and advice for preparation
Review
Example problemsSlide2
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Webassign
questions – Assignment #15
Consider the sinusoidal wave of the figure below with the wave function
y
= 0.150 cos(15.7x − 50.3
t
)
where
x
and y are in meters and t is in seconds. At a certain instant, let point A be at the origin and point B be the closest point to A along the x axis where the wave is 43.0° out of phase with A. What is the coordinate of B? Slide4
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Webassign
questions – Assignment #15
A transverse wave on a string is described by the following wave function.
y
= 0.115 sin ((π/9)
x
+
5
πt)where x and y are in meters and t is in seconds. Determine the transverse speed at t = 0.150 s for an element of the string located at x = 1.50 m.(b) Determine the transverse acceleration at
t = 0.150 s for an element of the string located at x = 1.50 m.Slide5
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Webassign
questions – Assignment #15
A sinusoidal wave in a rope is described by the wave function
y = 0.20 sin (0.69
πx
+ 20
πt
)
where x and y are in meters and t is in seconds. The rope has a linear mass density of 0.230 kg/m. The tension in the rope is provided by an arrangement like the one illustrated in the figure below. What is the mass of the suspended object?
T
mgSlide6
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Comment about exam on Tuesday 10/29/2013Slide7
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iclicker
question
What is the purpose of exams?
Pure pain and suffering for all involved.
To measure what has been learned.
To help students learn the material.
Other.Slide8
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Advice on how to prepare for the exam
Review lecture notes and text chapters 9-13,15-16
Prepare equation sheet
Work practice problems
Topics covered
Linear momentum
Rotational motion and angular momentum
Gravitational force and circular orbits
Static equilibrium
Simple harmonic motion
Wave motionSlide9
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What to bring to exam:
Clear head
Calculator
Equation sheet
Pencil or penSlide10
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iclicker
question:
Have you looked at last year’s exams?
A. Yes B. NoSlide11
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Linear momentum
What is it?
When is it “conserved”?
Conservation of momentum in analysis of collisions
Notion of center of mass Slide12
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Linear momentum -- continued
Physics of composite systemsSlide13
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Example – completely
inelastic
collision; balls moving in one dimension on a frictionless surfaceSlide14
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Examples of two-dimensional collision;
balls
moving on a frictionless surfaceSlide15
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The notion of the center of mass and the physics of composite systemsSlide16
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Finding the center of massSlide17
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Rotational motion and angular momentum
Angular variables
Newton’s law for angular motion
Rotational energy
Moment of inertia
Angular momentum
qSlide18
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Review of rotational energy associated with a rigid bodySlide19
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Moment of inertia:Slide20
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CM
CMSlide21
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iclicker
exercise:
Three round balls, each having a mass M and radius R, start from rest at the top of the incline. After they are released, they roll without slipping down the incline. Which ball will reach the bottom first?
A
B
CSlide22
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How
can you make
objects
rotate?
Define torque:
t
=
r
x F t = rF sin q
r
F
q
q
F
sin
qSlide23
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Example form
Webassign
#11
X
t
1
t
3
t
2
iclicker
exercise
When the pivot point is O, which torque is zero?
A.
t
1
?
B.
t
2
?
C.
t
3
?Slide24
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Vector cross product; right hand ruleSlide25
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From Newton’s second law – continued – conservation of angular momentum:Slide26
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Example of conservation of angular momentumSlide27
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Summary – conservation laws we have studied so far
Conserved quantity
Necessary condition
Linear momentum
p
F
net
= 0
Angular momentum Ltnet = 0Mechanical energy E
No dissipative forcesSlide28
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Fundamental gravitational force law and planetary motion
Newton’s gravitational force law
Gravity at Earth’s surface
Circular orbits of gravitational bodies
Energy associated with gravitation and orbital motionSlide29
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Universal law of gravitation
Newton (with help from Galileo,
Kepler
, etc.) 1687Slide30
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Gravitational force of the Earth
R
E
m
Note: Earth’s gravity acts as a point mass located at the Earth’s center.Slide31
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Stable circular orbit of two gravitationally attracted objects (such as the moon and the Earth)
R
EM
F
a
vSlide32
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m
1
R
2
R
1
m
2
v
1
v
2
Circular orbital motion about center of mass
CMSlide33
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m
1
R
2
R
1
m
2
v
1
v
2
L
1
=m
1
v
1
R
1
L
2
=m
2
v
2
R
2
L = L
1
+ L
2
Note: More generally, stable orbits can be elliptical.Slide34
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Gravitational potential energy
Example:Slide35
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Analysis of static equilibrium
Meanwhile – back on the surface of the Earth:
Conditions for stable equilibriumSlide36
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36Slide37
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T
Mg
mg
**
XSlide38
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Some practice problemsSlide39
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From
webassign
:
A 100-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.800 rev/s in 2.00 s? (State the magnitude of the force.)
F
R
view from top:Slide41
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From
webassign
:
A 10.3-kg monkey climbs a uniform ladder with weight
w = 1.24 102 N and length
L
= 3.35 m as shown in the figure below. The ladder rests against the wall and makes an angle of
θ
= 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N.