Energy Spring 09

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Chapter 3

• Energy (Spring 09)

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What 4-letter word in the English language upsets
more people than any other?

• Especially college students

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Work

• Work is defined as being the product of a force
  and the distance the force moves in the direction
  of the force.
• Movement must happen in the direction of the
  force.
• The force and the motion cannot be perpendicular.
• No work is done in holding something.
• No work is done in carrying something parallel to
  the ground.
• No work is done in doing physical science
  homework unless a pencil or pen is pushed along
  the paper.

4
Work

• Work force x distance moved
• W F d (put on formula sheet)
• What work is done when a force of 10 N is used to
  push an object 3 m?
• Note that the weight or mass of the object is not
  important, only the force necessary to move it.

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The joule

• 1 joule 1 newton 1 meter
• A joule is the work done in pushing with a force
  of one newton for a distance of one meter.
• James Prescott Joule was an English brew-master.
  We will hear more of him later.
• 3q

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Work against gravity

• Work force x distance
• When we lift something, the force necessary to
  lift it is the weight of the object
• wmg (force)
• Therefore, the work necessary to raise an object
  a height h is
• Wmgh (formula sheet) work
• h is the height the object is raised (or
  lowered).
• The weight is wmg, dont confuse weight and
  work. Weight is a force that can do work.

7
Calculate the amount of work for a 100 kg person
to climb stairs that are 10 m high.

• Data
• W?
• m100 kg
• h10 m

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How fast can you work?

• Power is the rate of doing work.
• Power work/time
• Formula sheet!
• If 30 joules of work is done in 6 seconds, what
  is the power?

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Units of power

• One watt is one joule per second.
• Watt joule/sec
• 5 watts 5 w

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What is my power if my mass is 70 kg and I can
climb stairs that are 10 m high in 3 seconds?
One horsepower is 746 watts so 2286 W is 3.1
horsepower. This calculation is necessary for
your pre-lab next week (measure your
horsepower). Note that this says nothing about
how steep the stairs are, only their height. 2q
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Suggestions to improve the class.

• Clicker doesn't work
• Slow down
• Present more challenging material
• Room too hot/cold
• More class interaction
• Too much talking in the back of the room
• Give more CPS questions

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If I have a lot of energy I can do a lot of work.

• Energy is the ability (capacity) to do work.
• Energy comes in many forms
• Heat energy
• Chemical energy
• Food
• Gasoline
• Dynamite
• Potential energy
• Kinetic energy

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Potential energy

• Potential energy is energy due to the position of
  an object.
• Examples of potential energy include
• A compressed spring
• A nail near a magnet
• A car on a hill
• Gravitational potential energy

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Gravitational Potential Energy

• Energy work done
• To have one joule of energy, I must do 1 joule of
  work to raise the object.
• The units of work are also joules.
• The force of gravity is mass times the
  acceleration of gravity
• W mg

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Gravitational P.E. (cont)

• P.E. Work force distance
• W f d
• f Weight W mg
• d distance height h
• P.E. mgh (Formula for gravitational potential
  energy)
• This applies only on the surface of the
  Earth.

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Gravitational P.E. (cont)

• What is the P.E. of a 20 kg block, 2 m above the
  floor?

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Kinetic Energy

• Kinetic energy is the energy something has
  because it is moving.
• Energy of motion
• K.E. ½ mv2
• Where m mass of the object
• v velocity of the object

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Kinetic energy

• What is the K.E. of a 70 kg person running 10
  m/s?

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Energy a review

• Energy the ability to do work
• Potential energy P.E. mgh
• Kinetic energy K.E. ½ mv2

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Conservation of Energy

• Energy may be changed from one type to another
  but the total amount of energy remains the same.

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More on conservation of energy

• Total energy is always conserved
• We will be especially interested in situations in
  which mechanical energy is conserved
• This means no energy is given to heat or friction
• When mechanical energy is conserved, the sum of
  the potential and the kinetic energies will
  remain constant.
• There are many types of problems we can solve
  using this knowledge.
• This will be the idea that will be worth more
  points on the next two tests than any other topic.

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Energy conservation- Changing P.E. to K.E. and
K.E. to P.E. - - - - Case 1 A falling object

• 100 P.E at the top
• 90 P.E. 10K.E.
• 80 P.E. 20K.E
• 70 P.E. 30K.E
• 60 P.E. 40K.E
• 50 P.E. 50K.E half way down
• 40 P.E. 60K.E
• 30 P.E. 70K.E
• 20 P.E. 80K.E
• 10 P.E. 90K.E
• . 100K.E at the bottom

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P.E. to K.E. and K.E. to P.E.

• At the top All P.E.
• 1/3 of the way from the top 2/3 P.E., 1/3 K.E.
• Half way down ½ K.E., ½ P.E.
• 1/3 of the way from the bottom, 1/3 P.E., 2/3
  K.E.
• At the bottom All K.E.

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Potential to Kinetic

• What is the velocity of an object after falling
  10m?
• v?
• h 10m
• Initial state Potential energy
• Final state kinetic energy
• Principle P.E. K.E.

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You will be asked to add one additional step in
the solution of these problems.
That step is the principle.
In the principle you must give the state of the
energy of the system in its initial state and its
final state.
For this problem the principle is Potential
Energy is changed to Kinetic Energy.
mgh ½ mv2
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Potential to Kinetic

• What is the velocity of an object after falling
  10m?
• v?
• h 10m
• Initial state Potential energy
• Final state kinetic energy
• Principle P.E. K.E.
• mgh ½ mv2

3q
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Kinetic to Potential

• How high will an arrow go that is shot straight
  into the air with an initial velocity of 100 m/s?
• h ?, v 100 m/s
• Initial state kinetic energy
• In this problem the arrow has already been shot
  and is moving with a velocity of 100 m/s.
• But it is still at zero height.
• final state potential energy
• ½ mv2mgh
• Solve the equation for h

3q
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The energy can be used to do work or work can be
used to give energy.

• Work to Kinetic energy
• Work to Potential energy
• Kinetic energy to work
• Potential energy to work

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Work to energy and energy to work

• A 3 kg hammer moving 10 m/s hits a nail and
  drives it 2 cm into a board. What was the force
  on the nail?
• m 3 kg v 10 m/s d 2 cm 0.02 m F?
• A falling hammer (K.E.) drives a nail
  (work)(force x distance)
• Principle K.E. work
• ½ mv2Fd

3q
30
How fast will a 5 kg rocket be traveling if its
motor has a force of 2000 n and it operates for
500 m horizontally?

• v?, m5kg, F2000N, d500m
• Principle work K.E.
• Fd½ mv2
• v?
• m5kg
• F 2000 n
• d 500 m

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Benefits of groups (from Fall 2007)

• 26 students are currently in groups
• On Test one, these students received a total of
  212 bonus points
• The 5 participants of one group each received 22
  points (the max on this test (10).
• The way to receive maximum benefit is to work
  together and help each other understand as the
  material is covered in class.
• If any one would like to join but doesn't have a
  group, send me an email or talk to me and I will
  help you find a group.

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Work to energy and energy to work

• A 3 kg hammer moving 10 m/s hits a nail and
  drives it 2 cm. What was the force on the nail?
• m 3 kg v 10 m/s d 2 cm 0.02 m F?
• A falling hammer (K.E.) drives a nail
  (work)(force x distance)
• Principle K.E. work
• ½ mv2Fd

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How fast will a 5 kg rocket be traveling if its
motor has a force of 2000 n and it operates for
500 m?

• v?, m5kg, F2000N, d500m
• Principle work K.E.
• Fd½ mv2
• v?
• m5kg
• F 2000 n
• d 500 m

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Conservation of momentum

• Two types Linear momentum and angular momentum
• Linear momentum mass times velocity
• In the absence of outside forces, the total
  momentum of a group of objects remains unchanged
  (even if the objects collide).
• Useful when objects collide or when they separate
  (boy jumping from wagon, etc)
• Angular momentum radius x mass x velocity
• Useful for systems, such as planets, comets, etc
• We will only do calculations with linear momentum.

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momentum before collision momentum after
m1
v1i
m2
v2i

• m1 is the mass of object one.
• v1i is the initial velocity of object one.
• m2 is the mass of object two.
• v2i is the initial velocity of object two.
• v1f is the final velocity of object one.
• v2f is the final velocity of object two.
• m1 v1i m2 v2i m1 v1f m2 v2f

This needs to go on your formula sheet!
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• Example one
• A 500 kg car traveling 20 m/s collides head-on
  with a 2000 kg truck traveling 10 m/s in the
  opposite direction. The two stick together after
  the collision. What is the direction and
  velocity of the two after the collision?

DATA
This minus sign is very important
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• General equation
• m1 v1i m2 v2i m1 v1f m2 v2f
• In our special case (v1f v2f vf )
• m1 v1i m2 v2i (m1 m2)vf
• 500 kg20 m/s 2000 kg(-10 m/s)(5002000)kgvf
• 10,000 kg m/s-20,000 kg m/s 2500 kg vf
• -10,000 kg m/s 2500 kg vf
• vf -10,000 kg m/s
• 2500 kg
• vf -4 m/s Direction is that of the truck

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Another momentum example

• A 70 kg man stands on a 20 kg boat in the water
  and jumps with a velocity of 5 m/s. What is the
  recoil velocity of the boat?

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• General equation
• m1 v1i m2 v2i m1 v1f m2 v2f
• In our special case (v1i v2i 0 )
• 0 m1 v1f m2 v2f
• - m1 v1f m2 v2f
• -70 kg5 m/s 20 kgvf
• vf -350 kg m/s
• 20 kg
• vf -17.5 m/s Direction is opposite the
  way the man jumped.

The minus sign tells us the direction.
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Caloric

• A colorless, odorless liquid that is in most
  substances.
• When a substance burns the caloric in it is given
  off as heat
• This theory explained heat until the 18th
  century.

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Benjamin Thompson

• An American who fled the U.S. in 1773 because of
  British sympathies.
• Became a military consultant (mercenary)
• Took the name of Count Rumford
• Made cannon
• Discovered that heat is a form of energy
• Set up the first public school for the children
  of his workers.

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James Prescott Joule

• An rich English beer maker who liked to do
  science experiments.
• James Prescott Joule showed how many joules (unit
  of energy) were in a calorie (unit of heat).
• 1 calorie 4.2 joules (put on formula sheet)
• 1 calorie is the amount of heat necessary to
  raise the temperature of one gram of water one
  degree Celsius.

43
Guess who

• Didnt like grade school very well
• Got a doctors degree in physics but couldnt get
  a job teaching (even in high school) so took a
  job in the post office (taking care of patents).
• Takes his girl friend on a trip and she gets
  pregnant.
• Child is taken by girls relatives, and is not
  heard of later
• Writes three papers in physics journals in 1905
  that profoundly change three major areas of
  physics.
• Becomes most famous scientist of 20th century

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Albert Einstein

• Theory of Brownian motion
• Theory of photons
• Theory of relativity
• Two postulates of special relativity
• The speed of light is always measured to be the
  same even when two systems are moving with
  respect to one another.
• The laws of physics apply in systems that are
  moving with respect to one another.

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• Using these two postulates and some algebra the
  following results apply for the case in which two
  systems are moving with respect to one another
  with a relative speed close to speed of light
• The following happen (and have been proven to
  take place by experiments in the laboratory).
• Length is measured to be different (shorter)
• Mass is measured to be greater
• Time is measured to be longer
• Mass can be changed to energy
• E mc2

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General Theory of Relativity

• The special theory that we have already discussed
  does not apply to systems that are accelerated or
  in a gravitational field.
• The general theory applies to accelerated systems
  or systems in a gravitational field.
• The most significant result of the general theory
  we will note is that gravity affects light.
• Light is bent by gravity (stars)
• We can see this when there is an eclipse of the
  sun.

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E mc2

• E Energy
• m mass
• c speed of light 3 x 108 m/s (formula sheet)
• c2 9 x 1016 m2/s2
• What energy is obtained when 7 grams is changed
  to mass
• Data m 7 grams 0.007 kg

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The Energy Problem

• Energy is necessary for our life style.
• We are running out of the energy sources we use
  the most.

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Fossil Fuels

• The cheapest
• The easiest to use
• The most convenient
• The worst for the environment (Global warming and
  acid rain)
• Supplies will become limited in our lifetime.

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Energy Costs per kilowatt hour of electricity

• Natural gas 3-4
• Coal 4-5
• Wind 4-5
• Geothermal 3-8
• Hydropower 4-10

• Biomass 6-8
• Nuclear 10-15
• Solar thermal 10-15
• Photovoltaics 20-30

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Solar generated hydrogen

• Burns without pollution
• H2 O2 ? H2O
• Could be used in cars and distributed at filling
  stations
• Car manufacturers are designing hydrogen cars

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Cars without engines Each wheel has an electric
motor that drives it
Skateboard concept All electronic steering,
brakes Tops plug-in to the fuel cell base.
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2q
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Best possibilities for the future

• Conservation
• Energy efficient cars/trucks
• Better insulated houses
• Methane hydrate
• Methane (natural gas) combined with water
• Uncertain quantities
• In difficult places to access
• Increased use of wind and solar energies
• Hydrogen powered cars/trucks
• Fusion

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Nuclear energy

• Good or Bad?
• Two types
• Fission (to split apart) (Atomic bomb)
• Uses Uranium as a fuel
• What we now have
• All present nuclear power plants use fission
• Fusion (to join together) (Hydrogen bomb)
• A possibility for the future
• Uses hydrogen as a fuel (sea water)

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Fission

• Fuel is uranium (which splits apart)
• Good points
• No CO2
• No radioactivity in normal operation
• In normal operation a nuclear power plant
  releases much less radioactivity than a coal
  burning plant.
• Bad points
• Possibility of an accident (Chernobyl)
• Disposing of spent (used) fuel

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Fusion

• Fuel is hydrogen (not radio-active)
• Good points
• Produces tremendous amounts of energy
• Very good for the environment
• Uses ocean water for fuel
• Bad points
• We dont know how to do it yet.

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Conservation of energy revisited

• This will be the problem on the chapter 3 and
  chapter 4 tests that will be worth the most
  points.

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Energy conservation- Changing P.E. to K.E. and
K.E. to P.E. - - - - Case 1 A falling object

• 100 P.E at the top
• 90 P.E. 10K.E.
• 80 P.E. 20K.E
• 70 P.E. 30K.E
• 60 P.E. 40K.E
• 50 P.E. 50K.E half way down
• 40 P.E. 60K.E
• 30 P.E. 70K.E
• 20 P.E. 80K.E
• 10 P.E. 90K.E
• . 100K.E at the bottom

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P.E. to K.E. and K.E. to P.E.

• At the top All P.E.
• 1/3 of the way from the top 2/3 P.E., 1/3 K.E.
• Half way down ½ K.E., ½ P.E.
• 1/3 of the way from the bottom, 1/3 P.E., 2/3
  K.E.
• At the bottom All K.E.
• It is very important to note that the total
  energy is always the same
• Total Energy Potential Energy Kinetic Energy
• (True when there is no friction and no work
  done).
• In the end, the energy will be all heat energy!

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Calculate the work necessary to raise an 10 kg
rock 30 m high. (25 point problem)

• Data m 10 kg, h 30 m, Work?
• WFdmgh10kg9.8m/s230m 2940j
• What is the potential energy at this height
  (30m)?
• No calculation is necessary, the P.E. is 2940J.
• What is the kinetic energy at this height?
• No calculation is necessary, as the rock is
  sitting still, the K.E. is zero!
• Total energy K.E. P.E. 2940j at all heights.

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• What is the total energy at this height?
• No calculation is necessary, T.E. is 2940j.
• Calculate the P.E., the K.E. and the T.E when the
  rock is 10 m from the ground and when it just
  begins to touch the ground (the height is zero
  and the velocity is maximum).
• The total energy remains the same in all cases,
  2940j,
• At ground level, h0 so P.E. is zero, thus the
  K.E. is 2940j

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• To calculate the P.E. at 10 m height,
• Data m10 kg, h10m, P.E.?
• P.E. mgh 10kg9.8m/s210m 980j
• The K.E. at this point is
• K.E. T.E. P.E. 2940j 980j 1960j
• What is the heat energy produced when the rock
  hits the ground?
• No calculation is necessary, all the energy is
  changed to heat, so the answer is 2940j.

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The energy can be used to do work or work can be
used to give energy. The Principle

• Work to Kinetic energy
• Work to Potential energy
• Kinetic energy to work
• Potential energy to work
• Potential energy to Kinetic energy
• Kinetic energy to Potential energy

69
A 3 kg hammer moving 10 m/s hits a nail and
drives it 2 cm. What was the force on the nail?

• Data
• m 3kg, v 10 m/s, d 0.02 m, F?
• Principle
• Initial K.E Final work
• ½ mv2Fd

70
How fast will a 5 kg rocket be traveling if its
motor has a force of 2000 n and it operates for
500 m?

• Data
• V?, m5kg, F 2000 N, d500m
• Principle
• Initial state work Final state K.E.
• Fd ½ mv2
• V 632 m/s

71
Potential Energy to Kinetic Energy

• What is the speed of a ball that has fallen 2 m
  without friction?
• In the beginning all the energy is P.E.
• P.E. mgh
• After falling 2 m, all the energy is Kinetic
• K.E. ½ mv2
• K.E. P.E.
• ½ mv2 mgh
• v v2gh
• v v29.8 m/s22 m v39.2 m2/s2 6.26 m/s

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Density help for your pre-lab

• Density is the mass per unit volume.
• Density mass/volume
• Dm/v

73
Calculate the density of a wood cylinder of
diameter 6 cm, length 10 cm and mass 250 grams.

• Data d 6 cm, (r 3 cm), L 10 cm and m 250
  g.