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© 2012 Pearson Education, Inc. Slide 1-1

PreClass Notes: Chapter 4, Sections 4.5,4.6

• 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.

© 2012 Pearson Education, Inc. Slide 1-2

Outline

• 4.5 Solving Force Problems

• 4.6 Newton’s Third Law,

• The Normal Force

• Hooke’s Law

“Using Newton’s second law

with multiple forces is easier if

we draw a free-body diagram.”

– R.Wolfson

Image from http://physicstasks.eu/380/a-girl-pulls-a-sledge-on-some-snowy-pavement

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© 2012 Pearson Education, Inc. Slide 1-3

Drawing a Free-Body Diagram

• When solving a problem in which multiple forces act

on an object, you should:

1. Identify the object of interest.

2. List all the forces that are acting on that object.

3. Represent the object as a dot.

4. Draw the vectors for only those forces acting on

the object, with their tails all starting on the dot.

© 2012 Pearson Education, Inc. Slide 1-4

Example 4.3

A 740-kg elevator accelerates

upward at 1.1 m/s2, pulled by a

cable of negligible mass. Find the

tension force in the cable.

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© 2012 Pearson Education, Inc. Slide 1-5

Forces and Interactions

Interaction

• is between one thing and another.

• requires a pair of forces acting on two objects.

Example: interaction of hand and wall pushing on each other

Force pair—you push on wall; wall pushes on you.

© 2012 Pearson Education, Inc. Slide 1-6

Newton’s Third Law of Motion

If object A exerts a force on object B, then object B

exerts an oppositely directed force of equal

magnitude on A.

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© 2012 Pearson Education, Inc. Slide 1-7

Action and reaction forces

• one force is called the action force; the other

force is called the reaction force.

• are co-pairs of a single interaction.

• neither force exists without the other.

• are equal in strength and opposite in direction.

• always act on different objects.

© 2012 Pearson Education, Inc. Slide 1-8

• Reexpression of Newton’s third law:

To every action there is always an

opposed equal reaction.

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© 2012 Pearson Education, Inc. Slide 1-9

Got it?

• If you exert a force 𝐹 on a bookcase, the force

which the bookcase exerts on you

A. is always − 𝐹 .

B. depends on your mass.

C. depends on the mass of the bookcase.

D. depends on the acceleration of the bookcase.

E. depends on the speed of the bookcase.

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• Not every pair of equal and opposite forces form a third-law

pair.

• The two forces on the block act on the same object, so

they cannot be a third-law pair.

• They happen to be equal and opposite, but not because of

Newton’s Third Law.

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• Below is the same block on a tilted table.

• In this case those same two forces are clearly not equal

and opposite.

• The forces do not cancel, and the block accelerates.

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• The gravitational forces on you and

Earth do form a third-law pair.

• [Figure not to scale.]

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Example

• What is the net force on the 3 kg block?

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Elasticity

Hooke’s law: The extension of a spring is directly

proportional to the force applied to it.

extension~Force or x~F D

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Tension and Compression

When something is

• pulled it is in tension.

• squashed it is in compression.

[Image retrieved Jan.11 2013 from

http://busstop.typepad.com/blog/2007/07/the-blonde-and-.html ]

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Hooke’s Law

• A stretched or compressed spring produces a restoring

force in a direction is opposite that of the stretch or

compression.

• In an ideal spring, the stretch or compression is directly

proportional to the force exerted by the spring:

• k is called the spring constant of the spring [N/m]

• The negative sign is there to remind you that the force 𝐹𝑠exerted by the spring on the object is opposite in direction to

the displacement 𝑥 of the end of the spring from its normal

position.

• Springs provide convenient devices for measuring force.

𝐹𝑠 = −𝑘𝑥

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© 2012 Pearson Education, Inc. Slide 1-17

Chapter 4 Big Ideas

• Force causes change in motion, not motion itself.

• Uniform motion (straight line, constant speed) needs no

cause or explanation.

• Any deviation in speed or direction requires a net force.

• Forces always come in pairs: Every interaction between two

objects consists of two forces which are equal in magnitude

but opposite in direction.