Transcript 08_LectureOutlines
Chapter 8 Equilibrium and Elasticity
Topics:
•
Torque and static equilibrium
• • • •
The spring force Hooke’s law Elastic materials The elastic limit Sample question: How does a dancer balance so gracefully
en pointe
? And how does her foot withstand the great stresses concentrated on her toes?
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Slide 8-1
Reading Quiz
1. An object is in equilibrium if A.
B.
F
net net = 0 = 0.
C. either A or B.
D. both A and B.
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Slide 8-2
Answer
1. An object is in equilibrium if D. both A and B.
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Slide 8-3
Reading Quiz
2. An object will be stable if A. its center of gravity is below its highest point.
B. its center of gravity lies over its base of support. C. its center of gravity lies outside its base of support.
D. the height of its center of gravity is less than 1/2 its total height.
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Slide 8-4
Answer
2. An object will be stable if B. its center of gravity lies over its base of support. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 8-5
Reading Quiz
3.
Hooke’s law describes the force of A. gravity.
B. a spring.
C. collisions.
D. tension.
E. None of the above.
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Slide 8-6
Answer
3.
Hooke’s law describes the force of B. a spring.
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Slide 8-7
Torque and Static Equilibrium
For an extended object to be in equilibrium, the net force
and
the net torque must be zero.
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Slide 8-8
Choosing the Pivot Point
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Slide 8-9
Solving Static Equilibrium Problems
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Slide 8-10
Checking Understanding
What does the scale read?
A.
B.
C.
D.
500 N 1000 N 2000 N 4000 N Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 8-11
Answer
What does the scale read?
C.
2000 N Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 8-12
Example
A 2-m-long board weighing 50 N extends out over the edge of a table, with 40% of the board’s length off the table. How far beyond the table edge can a 25 N cat walk before the board begins to tilt?
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Slide 8-13
The Spring Force
The
magnitude
of the spring force is proportional to the displacement of its end:
F
sp =
k
∆
x
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Slide 8-14
Hooke’s Law
The spring force is directed oppositely to the displacement. We can then write
Hooke’s law
as (
F
sp )
x
= –
k
∆
x
Slide 8-15 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Checking Understanding
Which spring has the largest spring constant?
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Slide 8-16
Answer
Which spring has the largest spring constant?
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Slide 8-17
Checking Understanding
The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude?
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Slide 8-18
Answer
The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude?
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Slide 8-19
Example
A 20-cm-long spring is attached to a wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant?
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Slide 8-20
Example
The same spring is now used in a tug-of-war. Two people pull on the ends, each with a force of 100 N. How long is the spring while it is being pulled?
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Slide 8-21
Example
A spring with spring constant
k
= 125 N/m is used to pull a 25 N wooden block horizontally across a tabletop. The coefficient of friction between the block and the table is
µ
k = 0.20. By how much does this spring stretch from its equilibrium length?
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Slide 8-22
The Springiness of Materials: Young’s Modulus
The force exerted by a stretched or compressed rod has the same form as Hooke’s law:
K
U
g
Y
is
Young’s modulus
, which depends on the material that the rod is made of.
Slide 8-23 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Bending Beams
U
g
K
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Slide 8-24
Beyond the Elastic Limit
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Slide 8-25