I estimate my grade on exam 2 to be:

1
I estimate my grade on exam 2 to be
Physics 1710Warm-up Quiz

0

• A
• B
• C
• D
• N/A
• F

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Physics 1710Chapter 13 Apps Gravity
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• Center of Gravity (comparison)

CM
CM
Ball Fg - mg
CG
Moon Fg - GmM/r2
3
Physics 1710Chapter 13 Apps Gravity
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• What is the mass of the earth?
• How do you know?

Peer Instruction Time
4
Physics 1710Chapter 13 Apps Gravity
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• What is the mass of the earth?
• How do you know? g?

Fg - mg
Fg - mg'
Peer Instruction Time
5
Physics 1710Chapter 13 Apps Gravity
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• 1' Lecture
• The moduli of elasticity (Y, E, B) characterizes
  the stress-strain relation
• stress modulus strain s Y e
• The force of attraction between two bodies with
  mass M and m, respectively, is proportional to
  the product of their masses and inversely
  proportional to the distance between their
  centers squared.
• Fg - rG Mm/d 2
• G 6.673 x 10 11 N m2 /kg2 2/3 x 10 10 N m2
  /kg2

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Physics 1710Chapter 13 Apps Gravity
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• Elasticity
• Definitions
• Stress s the deforming force per unit area.
• Strain e the unit deformation.
• Stress modulus x strain
• s F/A Y e

7
Physics 1710Chapter 13 Apps Gravity
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• Elasticity
• Stress s Strain e Curve

Stress s (N/m2)
s Y e
Strain e ?L/L ()
8
Physics 1710Chapter 13 Apps Gravity
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• Elasticity
• Stress s the deforming force per unit area.
• Strain e the unit deformation.
• Tensile/Compressive Stress Youngs Modulus E
• Stress modulus x strain
• s F/A E e E ?L/L

?L
L
s E e
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Physics 1710Chapter 13 Apps Gravity
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• Elasticity
• Stress s the deforming force per unit area.
• Strain e the unit deformation.
• Shear Modulus G
• Stress modulus x strain
• s F/A G e G ?x/h

L
?x
h
s
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Physics 1710Chapter 13 Apps Gravity
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• Elasticity
• Stress s the deforming force per unit area.
• Strain e the unit deformation.
• Hydraulic Stress Bulk Modulus B
• Stress modulus x strain
• s F/A p B e B ?V/V

?V
p
V
11
Which spring should have the larger spring
constant, a short spring (0.1 m long) or a longer
spring (0.3 m long)? F -k x
Physics 1710Chapter 13 Apps Gravity

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• k larger for shorter spring.
• k larger for longer spring.
• k the same for both springs.
• None of the above.

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Physics 1710Chapter 12 Apps Gravity
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• Solution

F -k x? s F/A E e E ?L/L F - A E x/
L k A E/L
What about a thicker (bigger A) wire?
13
Physics 1710Chapter 13 Apps Gravity
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• Isaac Newtons
• Universal Law of GravitationF - G M m/ d 2

d moon
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Physics 1710Chapter 13 Apps Gravity
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• Keplers Laws
• The orbits are ellipses. (Contrary to Aristotle
  and Ptolemy.)
• A central force F ? 1/ r 2 or r 2
• The areal velocity is a constant.
• Angular momentum is conserved
• ½ v r ?t constant implies that
• rmv L constant.
• T 2 ? r 3 implies F ? 1/ r 2, only.

?
r3
T 2
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Physics 1710Chapter 12 Apps Gravity
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• How did Newton figure out UL of G?
• Fact a moon circling a planet has an
  acceleration of a v 2 /r
• Fact a F/m.
• Fact Kepler had found that the square of the
  period T was proportional to the cube of the
  radius of the orbit r
• T 2 k r 3 .
• Thus
• v 2p r / T

16
Physics 1710Chapter 12 Apps Gravity

• And
• T 2 (2pr) 2 /(F r /m) k r 3
• Thus
• F (2p) 2 m/(k r 2 )
• An inverse square law, with k 1/ (2p) 2G
  M
• F G Mm/ r 2 ,
• But what value is G?

17
Physics 1710Chapter 13 Apps Gravity
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• Isaac Newtons
• Universal Law of GravitationF - G M m/ d 2

d moon
F g m g G M ? / R? 2
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Physics 1710Chapter 12 Apps Gravity

• Gravitation

g G M / R?2 G M ? gR ? 2 (9.80
N/kg)(6.37x10 6 m)2 3.99x10 14 N m 2/kg
Need to know G or M.
19
Physics 1710Chapter 13 Apps Gravity

• Henry Cavendish
• And the
• Cavendish Experiment

M
m
d
20
Physics 1710Chapter 13 Apps Gravity

• G 6.673 x 10 -11 N ?m 2 /kg 2
• G 2/3 x 10 -10 N ?m 2 /kg 2
• (to an accuracy of 0.1)

So, M ? (3.99x10 14 N m 2/kg)/(6.673 x 10-11 N
?m 2/kg 2) 5.98 x10 24 kg
21
Physics 1710Chapter 13 Apps Gravity

• Gravitational Force

F - G M m/ d 2 What is the order of magnitude
of the attraction between two people (m 100 kg)
separated by a distance of 1m?
M
m
d
22
What is the order of magnitude of the attraction
between two people (m 100 kg) separated by a
distance of 1m?
Physics 1710Chapter 13 Apps Gravity

• 9.8 N.
• 980. N
• 6.7 X 10 - 7 N
• 6.7 X 10 - 9 N
• None of the above

23
Physics 1710Chapter 13 Apps Gravity

• Gravitational Force

F - G M m/ d 2 F - (6.67 x10 11 N ?m 2 /kg
2)(100 kg)(100kg )/(1 m) 2 F - 6.67 x10 7 N
Equivalent weight F/g 67 ng
M
m
d
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Physics 1710Chapter 13 Apps Gravity

• Summary
• Keplers Laws
• The orbits of the planets are ellipses.
• The areal velocity of a planet is constant.
• The cube of the radius of a planets orbit
• is proportional to the square of the period.
• F - G M m/ d 2