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Chapter 7 Energy

Brent Royuk Phys-111

Concordia University

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Energy Introduction • What do you know? • Definition • Forms

– Potential – Kinetic

• The Unifying Idea • Top-Down vs.

Bottom-Up

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Energy Introduction

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Work • Definition

– The product of force and the distance moved due to that force

W = F d cos θ • The component in the direction of

motion – Advanced notation: – Work is a scalar

• Units

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W =! F ⋅! d

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Work •  Note: No motion = no work

–  Holding up a wall –  Carrying a book –  Satellites

•  What if you push a car at constant speed? •  Can work be negative?

– What if θ = 180o? •  Lifting work: Work = mgh

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Defining Energy –  The Work-Energy Definition Connection: Energy is the

capacity… •  Work is a process, and energy is a property of a system

–  Aristotle coined the word “energy” from the Greek for “at work.”

–  The Nearly Well-Know Dave Watson Definition •  “Energy is a property or characteristic (or trait or aspect?) of

matter that makes things happen, or, in the case of stored or potential energy, has the ‘potential’ to make things happen.”

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Feynman on Energy –  “It is important to realize that in physics today, we have no knowledge of

what energy is.” –Richard Feynman –  “There is a fact, or if you wish, a law, governing natural phenomena that

are known to date. There is no known exception to this law—it is exact so far we know. The law is called conservation of energy [it states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes]. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.” –Richard Feynman, Lectures on Physics, Vol. 1

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Kinetic Energy •  Equation: •  K is a form of energy: energy of motion •  Units? •  Note: K is a scalar.

–  But velocity is a vector!

•  Note v2 dependance. –  In a certain sense, speed matters more than mass

•  Compare: A 50 g arrow at 40 m/s with a 1 g bullet at 400 m/s.

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K =12

mv2

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The Work-Energy Theorem • W = Fx = max = m ((v2-vo

2)/2x)x = .5 mv2 - .5 mvo

2 = K - Ko = ΔK • Push an 8.0 kg sled a distance of

2.0 m with a force of 32 N. How fast is the sled moving? How much work is necessary to stop it?

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Variable Forces

•  For a spring,

•  A block with a mass m = 5.7 kg slides

on a horizontal frictionless table top with a constant speed v = 1.2 m/s. It is brought momentarily to rest by compressing a spring in its path. The spring constant k is 1500 N/m. How much is the spring compressed?

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W =12

kx2

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Power •  Definition:

– MKS Unit – Another common power unit: 1 hp = 746

W E = P t

•  kWh’s

•  Example – A crane lifts 1.0 metric ton 25 m in 9.0 s.

Find power in W, hp. How much energy would the crane use in 1.0 minute? How long would it take for the crane to do 100 kJ of work?

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P =Wt

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Conservative Forces •  For a conservative force, the

work it does is stored as energy that can be released later. – e.g. gravity, springs, electric

fields •  Conservative forces are

path-independent •  Nonconservative forces do

not store energy – e.g. friction –  longer path uses more energy

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Potential Energy •  Potential energy is energy of position:

symbol is U – Any system that wants to move: something

springy: springs, rubber bands, bent metal, item on a shelf, etc.

•  For spring: •  For gravity: U = mgy

–  the “spring of gravity” – Actually U = mgy - mgyo

•  You can define your “zero level” arbitrarily •  There’s nothing special about the floor, after all

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U =12

kx2

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Conservation of Mechanical Energy

•  In systems involving only conservative forces, mechanical energy is conserved. E = U + K = constant – Variants

Ko + Uo = K + U ΔK + ΔU = 0 Ebefore = Eafter

•  In a system with nonconservative forces, energy is lost Ko + Uo = K + U + Q

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Examples and Illustrations •  A marble in a bowl •  For an inclined plane, compare the work along

the plane with the work lifting an object to the same level. –  This is what all simple machines do: same work,

longer d --> smaller F (or vice versa) •  Pulleys, levers, etc.

•  Roller coaster –  A frictionless roller coaster leaves the top of a hill

from rest. At the top of the next hill, it is 15 m lower. How fast is it moving?

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Examples and Illustrations •  Pendulum

–  Pull a 1.0 m pendulum back 45o. How fast is it going at the bottom of the swing?

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Graphical Analysis

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Examples and Illustrations •  A skateboarder enters a ramp moving horizontally with

a speed of 6.5 m/s and leaves the ramp moving vertically with a speed of 4.1 m/s. Find the height of the ramp, assuming no energy loss due to frictional forces.

•  A baseball is thrown at some angle between zero and ninety degrees with a speed of 22 m/s. When it reaches its maximum height of 15 m, how fast is it moving?

•  Push a 10-kg box so it is sliding at 10 m/s. The coefficient of kinetic friction is 0.5. How far does it slide?

•  A skier with a mass of 80 kg starts from rest and skis down a slope from an elevation of 110 m. The speed at the bottom is 20 m/s. Analyze the energy of the system.

•  The Bowling Ball of Death

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Alternative Energy? Two types of Energy Therapy 1. Veritable (Measurable)

–  Magnet, Light, Sound, etc.

2. Putative (Bioenergy, Qi, Prana; Has not been measured)

–  Acupuncture, Qui Gong, Therapeutic Touch, Power Balance, etc.