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© 2010 Pearson Education, Inc.
PowerPoint® Lectures for
College Physics: A Strategic Approach, Second Edition
Chapter 8
Equilibrium
and Elasticity
© 2010 Pearson Education, Inc. Slide 8-2
8 Equilibrium and Elasticity
© 2010 Pearson Education, Inc. Slide 8-3
© 2010 Pearson Education, Inc. Slide 8-4
© 2010 Pearson Education, Inc.
Reading Quiz
1. An object is in equilibrium if
A. Fnet = 0.
B. net = 0.
C. either A or B.
D. both A and B.
Slide 8-5
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Answer
1. An object is in equilibrium if
A. Fnet = 0.
B. net = 0.
C. either A or B.
D. both A and B.
Slide 8-6
© 2010 Pearson Education, Inc.
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.
Slide 8-7
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Answer
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.
Slide 8-8
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Reading Quiz
3. Hooke’s law describes the force of
A. gravity.
B. a spring.
C. collisions.
D. tension.
E. none of the above.
Slide 8-9
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Answer
3. Hooke’s law describes the force of
A. gravity.
B. a spring.
C. collisions.
D. tension.
E. none of the above.
Slide 8-10
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Torque and Static Equilibrium
For an extended object to be in equilibrium, the net force
and the net torque must be zero.
Slide 8-11
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Choosing the Pivot Point
Slide 8-12
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Solving Static Equilibrium Problems
Slide 8-13
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Checking Understanding
What does the scale read?
A. 500 N
B. 1000 N
C. 2000 N
D. 4000 N
Slide 8-14
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Answer
What does the scale read?
A. 500 N
B. 1000 N
C. 2000 N
D. 4000 N
Slide 8-15
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Example Problem
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?
Slide 8-16
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Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
Slide 8-17
W
A
L
L
© 2010 Pearson Education, Inc.
Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
Slide 8-17
W
A
L
L
© 2010 Pearson Education, Inc.
Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
Slide 8-17
W
A
L
L
© 2010 Pearson Education, Inc.
Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
Slide 8-17
W
A
L
L
© 2010 Pearson Education, Inc.
Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
So what are the requirements for balance?
Slide 8-17
W
A
L
L
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Balance
For an object to balance, its center of gravity must reside over
its base of support. That way gravity does not exert a torque.
Base of support
Gravity acts at the
center of gravity.
Line of action
This force exerts no
torque about her toes.
Slide 8-18
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Stability of a Car
Slide 8-19
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Tiptoeing
Why can’t you stand on tiptoes if your toes are against a wall?
Center of gravity has to be over toes – the
base of support – to balance. That requires
shifting your body slightly forward. But you
can’t shift your body forward if your toes are
against the wall.
Slide 8-20
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The Spring Force
The magnitude of the spring force is proportional to the
displacement of its end:
Fsp = k ∆x Slide 8-21
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The spring force is directed oppositely to the displacement. We
can then write Hooke’s law as
Hooke’s Law
(Fsp)x = –k ∆x
Slide 8-22
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Checking Understanding
Which spring has the largest spring constant?
Slide 8-23
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Which spring has the largest spring constant?
Answer
A
Slide 8-24
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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?
Slide 8-25
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E. Not enough information to tell.
The same spring is stretched or compressed as shown below. In
which case does the force exerted by the spring have the largest
magnitude?
Answer
Slide 8-26
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Example Problem
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?
Slide 8-27
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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?
Example Problem
Slide 8-28
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The same spring is now suspended from a hook and a 10.2 kg
block is attached to the bottom end. How long is the stretched
spring?
Example Problem
Slide 8-29
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The Springiness of Materials: Young’s Modulus
The force exerted by a stretched or compressed rod has the
same form as Hooke’s law:
Y is Young’s modulus, which depends on
the material that the rod is made of.
Slide 8-30
YAF L
L
F LY
A L
stress
F
A strain
L
L
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Beyond the Elastic Limit
Slide 8-31
The stress
(F/A) at the
breaking
point is
called the
“tensile
strength”
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What hanging mass will stretch a 2.0-m-long, 0.50-mm-diameter
steel wire by 1.0 mm? Young’s modulus for steel is 20x1010 N/m2.
Example Problem
Slide 8-31ja-1
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What hanging mass will break a 2.0-m-long, 0.50-mm-diameter
steel wire by 1.0 mm? The tensile strength (maximum stress) for
steel is 1000x106 N/m2.
Example Problem
Slide 8-31ja-2
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Summary
Slide 8-32
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Summary
Slide 8-33
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Additional Example Problem
A spring with spring
constant k = 125 N/m
is used to pull a 25 N
wooden block
horizontally across a
tabletop at constant
speed. The coefficient
of friction between the
block and the table is
µk = 0.20. By how
much does this spring
stretch from its
equilibrium length?
Slide 8-34
