Post on 17-Oct-2021
transcript
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PreClass Notes: Chapter 12
• From Essential University Physics 3rd Edition
• by Richard Wolfson, Middlebury College
• ©2016 by Pearson Education, Inc.
• Narration and extra little notes by Jason Harlow,
University of Toronto
• This video is meant for University of Toronto
students taking PHY131.
Outline
“The key to the engineer’s success [in
making sure the Alamillo Bridge
doesn’t topple to the left] is static
equilibrium – the condition in which a
structure … experiences neither a net
force nor a net torque.”– R.Wolfson
• 12.1 Conditions for equilibrium
• 12.2 Center of Gravity
• 12.3 Static Equilibrium
Problems
• 12.4 Stability
Image from https://www.bluffton.edu/~sullivanm/spain/seville/calatravabridge/bridge.html ]
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Conditions for Static Equilibrium
• A system in static equilibrium undergoes neither
rotational nor linear acceleration.
– If it’s at rest, it remains at rest.
• The conditions for static equilibrium are:
– No net force:
– No net torque:
• Torques can be evaluated about any
convenient point.
0iF
0i i ir F
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• The figure shows three pairs of forces acting on an object.
Which pair, acting as the only forces on the object, results
in static equilibrium?
Got it?
A. Force pair
B. Force pair
C. Force pair
1 2+A A
1 2+B B
1 2+C C
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© 2012 Pearson Education, Inc. Slide 1-7
Center of Gravity
• The gravitational forces acting on all parts of an
object exert a torque on the object.
– These forces act like a single force, equal to the
object’s weight, acting at a point called the
center of gravity.
– In a uniform gravitational field, the center of
gravity coincides with the center of mass.
© 2012 Pearson Education, Inc. Slide 1-8
Finding the Center of Gravity
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© 2012 Pearson Education, Inc. Slide 1-9
Finding the Center of Gravity
© 2012 Pearson Education, Inc. Slide 1-10
Finding the Center of Gravity
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• The dancer in the figure is balanced; that is, she is in
static equilibrium. Which of the three lettered points
could be her center of gravity?
A. Point A
B. Point B
C. Point C
Got it?
Example 12.2 : At what angle will the ladder slip?
• Frictionless wall.
• Coefficient of
static friction with
the ground is μ.
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Stability
• An equilibrium is stable if a slight disturbance from
equilibrium results in forces and/or torques that tend to
restore the equilibrium.
• An equilibrium is unstable if a slight disturbance causes
the system to move away from the original equilibrium.
Cone on its base is stable Cone on its tip is unstable
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Kinds of Stability
Stable equilibrium: disturbed
ball will return to equilibrium
Metastable or conditionally stable
equilibrium: ball returns for small
disturbances, but not for large ones
Unstable equilibrium:
disturbed ball will leave
original equilibrium
Neutrally stable equilibrium
Conditions for Equilibrium and Stability
• To be in equilibrium, there must be zero net force on an object.
– Therefore the object must be at a maximum or minimum of its
potential energy curve:
• For stable equilibrium, the object must be at a minimum:
• The condition for unstable equilibrium is
dU
dx 0 (condition for equilibrium)
d 2U
dx2 0 (stable equilibrium)
2
20 (unstable equilibrium)
d U
dx
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Conditions for Equilibrium and Stability
In two and three
dimensions, an
object can be
stable in one
direction but not
another.