PHY 113 C Fall 2013 Lecture 14 1 PHY 113 C General Physics I 11 AM1215 PM MWF Olin 101 Plan for Lecture 14 Chapter 12 Static equilibrium Balancing forces and torques stability Center of gravity ID: 246934
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10/14/2013
PHY 113 C Fall 2013 -- Lecture 14
1
PHY 113 C General Physics I
11 AM-12:15 PM MWF Olin 101
Plan for Lecture 14:
Chapter 12 – Static equilibrium
Balancing forces and torques; stability
Center of gravity
Will discuss elasticity in Lecture 15 (Chapter 15)Slide2
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Newton’s law of gravitation:
Earth’s gravity:
Stable
circular orbits of gravitational attracted objects:
R
ES
F
a
v
M
sat
Summary of gravity:
R
E
mSlide4
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From
Webassign
Assignment #12:
When
a falling meteoroid is at a distance above the Earth's surface of 3.40 times the Earth's radius, what is its acceleration due to the Earth's gravitation?
m/s
2
towards earth
r=4.4R
E
mSlide5
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From
Webassign
Assignment #12:
An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 6.79 m/s
2. Determine the orbital period of the satellite.
rSlide6
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From
Webassign
Assignment #12:
How much work is done by the Moon's gravitational field as a 1090 kg meteor comes in from outer space and impacts on the Moon's surface?
R
M
iclicker
question
W>0
W<0Slide7
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From
Webassign
Assignment #12:
A space probe is fired as a projectile from the Earth's surface with an initial speed of 1.74 10
4 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth.
v
iSlide8
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From
Webassign
Assignment #12:
Plaskett's
binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v = 190 km/s and the orbital period of each is 10.7 days. Find the mass
M
of each star. (For comparison, the mass of our Sun is 1.99 10
30
kg.)Slide9
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PHY 113 C Fall 2013 -- Lecture 14
9
From
Webassign
Assignment #12:
Plaskett's
binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v = 190 km/s and the orbital period of each is 10.7 days. Find the mass
M
of each star. (For comparison, the mass of our Sun is 1.99 10
30
kg.)
iclicker
exercise:
Who might pose a question like this?
A mean professor.
A puzzle master.
An observational astronomer.Slide10
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Meanwhile – back on the surface of the Earth:
Conditions for stable equilibriumSlide11
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Stability of “rigid bodies”
N
m
i
gSlide12
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Center-of-mass
Torque on an extended object due to gravity (near surface of the earth) is the same as the torque on a point mass M located at the center of mass.
m
i
r
i
r
CMSlide13
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Notion of stability:
mg(-
j
)
r
T
q
F
=m
a
T- mg
cos
q = 0
-
mg sin
q = -
ma
q
t
=I
a
r mg sin
q
= mr
2
a =
mraq
Notion of equilibrium:
Example of stable
equilibrium for
q
» 0.Slide14
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Unstable equilibrium:
mg(-
j
)
r
T
q
Support
above
CM:
Support
below
CM:Slide15
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Nik
Wallenda
walking on high wire across Grand CanyonSlide16
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Analysis of stability:Slide17
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**
XSlide18
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**
X
F
g1
mg
R
CMSlide20
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iclicker
question:
F
1
F
2
Consider the above drawing of the two supports for a uniform plank which has a total weight Mg and has a weight mg at its end. What can you say about F
1
and F
2
?
F
1
and F
2
are both up as shown.
F
1
is up but F
2
is down.
F
1
is down but F
2
is up.
L/3
L
Mg
mgSlide21
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F
1
F
2
L/3
L
Mg
mg
**
XSlide22
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iclicker
question:
The fact that we found F
1
<0 means:
We set up the problem incorrectly
The analysis is correct, but the direction
of
F
1
is opposite to the arrow
Physics makes no sense
iclicker
question:
What would happen if we analyzed this problem by placing the pivot point
at F1 ?:The answer would be the same.
The answer would be different.
Physics makes no senseSlide23
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T
Mg
mg
**
XSlide24
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d
**
XSlide25
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mg
Mg
F
wall
N
T
Mg = 120 N
mg = 98 N
T < 110 N
**
XSlide26
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x
A ladder of weight Mg and of length L is supported by the ground with static friction force
f
and by a frictionless wall as shown. The firefighter has weight mg and is half-way up the ladder. Find the force that the ladder exerts on the wall.
q
**
X