for Physics Scientists & Engineers 1
Spring Semester 2008 Lecture 17
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Midterm Exam 1
Next Monday (February 11), we will have our first midterm exam in class All questions will be multiple choice The exam will cover chapters 1 -5, homework sets 1-5, and all the lectures through Friday You need to bring A calculator A No. 2 pencil to fill out the scantron form 1 sheet of size 8.5 x 11 in., with equations ("cheat sheet") Nothing else There will be a chart showing you which row to sit in by alphabetical order
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Energy, Work, Power
What we will learn today and this week: Kinetic energy is the energy contained in the motion of an object. Work is defined as energy transferred to an object or transferred from an object due to the action of a force. Positive work is defined as a transfer of energy to the object, and negative work is a transfer of energy from the object. Positive work is work done on the object, while negative work is work done by the object. Work is the scalar product of the force vector and the displacement vector. The change in kinetic energy due to a force is equal to the work done by the force. Power is the rate at which work is done
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Energy, the BIG PICTURE
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Energy in our Economy
Energy production Energy consumption Energy efficiency Energy resources National and global energy policy Needs informed citizens to join discussion
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Energy from Fossil Fuels
Fossil fuels Coal Oil Natural gas Basic chemical composition: Hydrocarbons Burning hydrocarbons with oxygen releases energy -> useful for power production on a very large scale Basis for most of our chemical industry as well Problems: Non-renewable resource Pollution: carbon dioxide emission: acid rain, global warming
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Solar Power
Radiation from Sun contains tremendous amounts of energy Guaranteed to be provided for next couple of billion years No pollution Use: Primary: solar cells
Solar farm in CA http://kjcsolar.com/aerial1.jpg
Secondary: wind, hydro
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"Renewable" Energy Sources
Wind Hydroelectric Geo-thermal Biomass (plants, animals)
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Energy from Nuclear Reactions
Reactions of atomic nuclei can liberate tremendous power Splitting (fission) of heavy nuclei (uranium,plutonium) Fusing hydrogen into helium Advantages: No greenhouse gas emission Practically infinite supply
Schematic drawing of ITER
Problems: Very dangerous radioactive waste needs very long term storage Potential for use in weapons of mass destruction
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Hydrogen Economy
Basic Idea: Produce hydrogen from renewable (or at least non-fossil) energy sources Burn hydrogen with oxygen into water Advantages Reduced pollution Reduced dependence on fossil fuels Challenges/problems Transport and storage Sufficient production of hydrogen (may need to invest more into nuclear power sources)
www.emagazine.com/january-february_2003/0103feat1.htm
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Clicker Question
How long will the world's oil resources last? A) B) C) D) E) 10 years 25 years 50 years 100 years 300 years
(this is a survey question, all answers will be given full credit)
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Prediction from DOE
50 years 100 years
You are here
http://www.eia.doe.gov/
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Energy and YOU
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Energy, Calories, Exercise
Organisms need regular energy supply for survival Caloric intake adds energy Physical activity "burns" energy Excess energy supply is stored as fat Weight loss only through reduction in caloric intake or increase in physical activity
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Let's Start at the Beginning: Kinetic Energy
Energy contained in the motion of an object Definition 2 1
K = 2 mv
2
Unit of kinetic energy:
This energy unit has received its own name, Joule (J), named after British physicist James Joule (1818-1889) Energy unit Useful conversion: 1 J = 1 N m
[K ] = [m] ![v] = kg m / s
2
2
1 J = 1 kg / m s
2
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Kinetic Energy Examples
Car of mass 1,310 kg driving 55 mph (=24.6 m/s)
K car = 1 mv 2 = 1 (1310 kg)(24.6 m/s)2 = 4.0 !10 5 J 2 2
Mass of the Earth is 61024 kg, and it orbits the Sun with a speed of 30,000 m/s K sun = 1 mv 2 = 1 (6.0 !10 24 kg)(3.0 !10 4 m/s)2 = 2.7 !10 33 J 2 2 Baseball (mass "5 ounces avoirdupois" = 0.142 kg) thrown at 80 mph (= 35.8 m/s) has kinetic energy K baseball = 1 mv 2 = 1 (0.142 kg)(35.8 m/s)2 = 91 J 2 2 Electron (me = 9.110-31 kg) moving with a speed of 1.3106 m/s (= 0.4% of the speed of light): K e = 1 mv 2 = 1 (9.1!10 "31 kg)(1.3 !10 6 m/s)2 = 7.7 !10 "19 J 2 2
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Other Energy Units
Atomic and nuclear physics introduced the electron-Volt
1 eV = 1.60210-19 J
(electron in previous example has ~5 eV kinetic energy) The energy you eat is measured in food calories
1 Cal = 4186 J
(1 Cal > 40 times the kinetic energy of the baseball in previous example) For very large energy measures one need a large unit. The energy released by one million tons of TNT is large
1 Mt = 4.01015 J
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Example: Falling Vase
Question: A crystal vase (mass 2.40 kg) is dropped from a height of 1.30 m and falls to the floor. What is its kinetic energy just before impact? Answer: Once we know the velocity of the vase just before impact, we can put it into our equation for the kinetic energy. To obtain this velocity, we remind ourselves of the kinematics of free-falling objects. 2 Use: v 2 = v0 ! 2g(y ! y0 ) = 2g(y0 ! y) (since v0 = 0) Now use definition of kinetic energy and obtain in this case:
K = 1 mv 2 = 1 m ( 2g(y0 ! y)) = mg(y0 ! y) 2 2
Numbers:
K = (2.40 kg) ! (9.81 m/s 2 ) ! (1.30 m " 0) = 30.6 J
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Example: Falling Vase - Observations
In the case of the falling vase, the kinetic energy is a function of the height (linearly dependent on height) from which the vase was released,
K = mg(y0 ! y)
Gravitational force, Fg = gm, accelerated vase during free fall, and thus increased its kinetic energy Kinetic energy is proportional to the magnitude of the gravitational force, too. Here the kinetic energy gained by the vase is simply the product of the magnitude of the gravitational force and the displacement.
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Work
Formal Definition:
Work is defined as energy transferred to an object or transferred from an object due to the action of a force. Positive work is defined as a transfer of energy to the object, and negative work is a transfer of energy from the object. Positive work is work done on the object, while negative work is work done by the object.
Please note: we have not specified what kind of energy is transferred. This work definition holds for all kinds of energy, but in particular also for kinetic energy
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Example: Vase on an Inclined Plane
Vase is sliding a distance r along the inclined plane (friction free sliding, for now) Introduce angle = 90-
Acceleration: a = g sin ! = g cos "
Kinetic energy
2 v 2 = v0 + 2a!r = 2g cos "!r #
(again v0=0)
K = 1 mv 2 = mg!r cos " 2
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Example: Vase on an Inclined Plane (2)
In this case, work (= change in kinetic energy) done on the vase by gravitational force is (a = angle between force and ! displacement !
K = mg!r cos " = Fg
!r cos "
Limiting cases: = 0 (force and displacement parallel): we
recover the result already derived for the case of the falling vase. = 90 (force perpendicular to displacement): no acceleration => no change in the kinetic energy => no work done by gravitational force on vase
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What exactly is energy?
Richard Feynman (1963): "It is important to realize that in
physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives `28' always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas."
Bottom line: WE DON'T KNOW WHAT ENEGY IS ... but it works great for calculating processes.
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