chapter 8n00006757/physicslectures/knight 2e/08_lect_outline/ja... · chapter 8 equilibrium and...

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PowerPoint® Lectures for

College Physics: A Strategic Approach, Second Edition

Chapter 8

Equilibrium

and Elasticity

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8 Equilibrium and Elasticity

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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

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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

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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

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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

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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

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Tiptoeing

Why can’t you stand on tiptoes if your toes are against a wall?

So what are the requirements for balance?

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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

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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

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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