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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. τnet = 0. C. either A or B. D. both A and B.

→

→

→

→

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Answer 1. An object is in equilibrium if

A. Fnet = 0. B. τnet = 0. C. either A or B. D. both A and B.

→

→

→

→

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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.

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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.

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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.

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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.

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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.

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Choosing the Pivot Point

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Solving Static Equilibrium Problems

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Checking Understanding What does the scale read?

A. 500 N B. 1000 N C. 2000 N D. 4000 N

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∑

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Answer What does the scale read?

A. 500 N B. 1000 N C. 2000 N D. 4000 N

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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.

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Stability of a Car: Critical angle

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1tan2cth

θ − =

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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.

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Tiptoeing Why can’t you stand on tiptoes if your toes are against a wall? Stated otherwise, what are the requirements for balance?

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Review: Hooke’s Law

An elastic system displaced from equilibrium oscillates in a simple way about its equilibrium position with

Simple Harmonic Motion.

Hooke’s Law describes the elastic response to an applied force.

Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion.

Ut tensio, sic vis - as the extension, so is the force

Importance of Simple Harmonic Oscillators

Simple harmonic oscillators are good models of a wide variety of physical phenomena

Molecular example If the atoms in the molecule do

not move too far, the forces between them can be modeled as if there were springs between the atoms

The potential energy acts similar to that of the SHM oscillator

Coupled Oscillators Molecules, atoms and particles are modeled as coupled oscillators.

Waves Transmit Energy through coupled oscillators. Forces are transmitted between the oscillators like springs

Coupled oscillators make the medium.

Hooke’s Law It takes twice as much force to stretch a spring twice as far.

The linear dependence of displacement upon stretching force:

appliedF kx=

Hooke’s Law Stress is directly proportional to strain.

( ) ( )appliedF stress kx strain=

+

Hooke’s Law: F = - k x

+

Hooke’s Law: F = - k x

+

Hooke’s Law: F = - k x

+

Hooke’s Law: F = - k x

+

Hooke’s Law: F = - k x

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The Spring Force

The magnitude of the spring force is proportional to the displacement of its end:

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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

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Checking Understanding Which spring has the largest spring constant?

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Which spring has the largest spring constant?

Answer

A

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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?

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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

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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?

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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

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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

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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. 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?

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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.

F = L L YA

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Beyond the Elastic Limit

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Summary

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Summary

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