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A child has two red wagons, with the rear one tied to the front by a stretchy rope (a spring). If the child pulls on the front wagon, the ____ increases.

  1. kinetic energy of the wagons
  2. potential energy stored in the spring
  3. both A and B
  4. not enough information

(c)

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A child has two red wagons, with the rear one tied to the front by a stretchy rope (a spring). If the child pulls on the front wagon, the energy stored in the system increases. How do the relative amounts of potential and kinetic energy in this system change over time?

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Which of the following are closed systems?

  1. Earth
  2. a car
  3. a frictionless pendulum
  4. a mass on a spring in a vacuum

(c), (d)

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Describe a real-world example of a closed system.

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A 5.0-kg rock falls off of a 10 m cliff. If air resistance exerts a force of 10 N, what is the kinetic energy when the rock hits the ground?

  1. 400 J
  2. 12.6 m/s
  3. 100 J
  4. 500 J

(a)

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Hydroelectricity is generated by storing water behind a dam, and then letting some of it run through generators in the dam to turn them. If the system is the water, what is the environment that is doing work on it? If a dam has water 100 m deep behind it, how much energy was generated if 10,000 kg of water exited the dam at 2.0 m/s?

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Before railroads were invented, goods often traveled along canals, with mules pulling barges from the bank. If a mule is exerting a 1200 N force for 10 km, and the rope connecting the mule to the barge is at a 20 degree angle from the direction of travel, how much work did the mule do on the barge?

  1. 12 MJ
  2. 11 MJ
  3. 4.1 MJ
  4. 6 MJ

(b)

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Describe an instance today in which you did work, by the scientific definition. Then calculate how much work you did in that instance, showing your work.

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Section summary

  • The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.
  • When all forms of energy are considered, conservation of energy is written in equation form as KE i + PE i + W nc + OE i = KE f + PE f + OE f size 12{"KE" rSub { size 8{i} } +"PE" rSub { size 8{i} } +W rSub { size 8{"nc"} } +"OE" rSub { size 8{i} } ="KE" rSub { size 8{f} } +"PE" rSub { size 8{f} } +"OE" rSub { size 8{f} } } {} , where OE size 12{"OE"} {} is all other forms of energy besides mechanical energy.
  • Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.
  • Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.
  • The efficiency Eff size 12{ ital "Eff"} {} of a machine or human is defined to be Eff = W out E in size 12{ ital "Eff"= { {W rSub { size 8{"out"} } } over {E rSub { size 8{"in"} } } } } {} , where W out size 12{W rSub { size 8{"out"} } } {} is useful work output and E in size 12{E rSub { size 8{"in"} } } {} is the energy consumed.

Conceptual questions

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See [link] .)

A car coasting downhill, moving over a crest then again moving downhill and finally stopping at a gas station. Each of these positions is labeled with an arrow pointing downward.
A car experiencing non-negligible friction coasts down a hill, over a small crest, then downhill again, and comes to a stop at a gas station.
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Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.

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Do devices with efficiencies of less than one violate the law of conservation of energy? Explain.

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List four different forms or types of energy. Give one example of a conversion from each of these forms to another form.

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List the energy conversions that occur when riding a bicycle.

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Problems&Exercises

Using values from [link] , how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays before they escaped and exposed viewers.)

4 × 10 4  molecules size 12{4 times "10" rSup { size 8{4} } " molecules"} {}

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Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Equating ΔPE g size 12{Δ"PE" rSub { size 8{g} } } {} and ΔKE size 12{Δ"KE"} {} , we obtain v = 2 gh + v 0 2 = 2 ( 9.80 m /s 2 ) ( 20.0 m ) + ( 15.0 m/s ) 2 = 24.8 m/s size 12{v= sqrt {2 ital "gh"+v rSub { size 8{0} rSup { size 8{2} } } } = sqrt {2 \( 9 "." "80"" m/s" rSup { size 8{2} } \) \( "20" "." 0" m" \) + \( "15" "." "0 m/s" \) rSup { size 8{2} } } ="24" "." 8" m/s"} {}

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If the energy in fusion bombs were used to supply the energy needs of the world, how many of the 9-megaton variety would be needed for a year’s supply of energy (using data from [link] )? This is not as far-fetched as it may sound—there are thousands of nuclear bombs, and their energy can be trapped in underground explosions and converted to electricity, as natural geothermal energy is.

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(a) Use of hydrogen fusion to supply energy is a dream that may be realized in the next century. Fusion would be a relatively clean and almost limitless supply of energy, as can be seen from [link] . To illustrate this, calculate how many years the present energy needs of the world could be supplied by one millionth of the oceans’ hydrogen fusion energy. (b) How does this time compare with historically significant events, such as the duration of stable economic systems?

(a) 25 × 10 6 years size 12{"25" times "10" rSup { size 8{6} } `"years"} {}

(b) This is much, much longer than human time scales.

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Questions & Answers

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
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hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
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money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
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Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
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Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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