Week 5

Focus on energy

Energy chapter from Physics for Future Presidents

 

Lec9Week5

Test Tuesay Oct 11,2011

 

ENERGY

 

There are several form of energy and some related concepts. To begin let us examine mechanical systems. Basically I am talking about blocks and balls. In particular we will start with a mass and a spring.

 

Energy of motion: Kinetic Energy

 

Energy is a simple number you can add to it or subtract it from an object. Basically the amount of KE an object contains is proportional to its mass and how fast it is moving. So when trying to figure out how much KE energy an object has you need to consider both factors. A car and a tennis ball have very different masses but they can both have the same KE but the tennis ball must be moving much faster than the car.

 

mass

v

 

 

KE

 

mass

v

 

 

KE

kg

m/s

mph

ftpmin

J

 

kg

m/s

mph

ftpmin

J

0.057

1.0

2.2

18.3

0.03

 

1000.00

0.01

0.02

0.14

0.03

 

5.0

11.2

91.4

0.71

 

 

0.04

0.08

0.69

0.7

 

10.0

22.4

182.9

2.9

 

 

0.08

0.17

1.4

2.9

 

100.0

223.7

1828.8

285.0

 

 

0.8

1.7

13.8

285.0

 

343.0

767.3

6272.8

3353.0

 

 

2.6

5.8

47.4

3353.0

 

 

 

 

 

 

 

 

 

 

 

 

The behavior and relationships are straightforward but foreing so we will consider money as an analog to energy.

KE is the energy an object carries Money in ones wallet.

 

PE:potential energy

This is a different form of energy. The book points out that the name could be confusing because it sounds like pseudo energy but this is a real from of energy. One type of potential energy is SPE: spring potential energy.

 

x stretched (compressed) distance from the relaxed state

 

Here we see that the more you stretch (compress) the spring the more energy is present in the spring.

To continue with our model we would like to add another form of money. We will consider money in our checking account as the analog to the SPE.

 

To apply this model we know that our total amount of money is the sum of the money in our wallet plus the amount in our checking account. These are two forms of money in the same way that we have two forms of energy. Lets add one more.

 

GPE: gravitational PE

h is the height of the object

For simplicity we will choose the lowest point in a problem to be h=0. We should become comfortable with the formula. Since this is a product of three values with one value g being a constant we can easily see how energy changes with mass m and height h. The higher something is the more energy it contains and the heavier it is the more energy it contains.

 

Gravity is sort of an invisible form of energy so we need to make it more real. The way the energy is stored is by adding energy to the gravitational field. There is a real place to put the energy. Although the formula is different, you can imagine an invisible spring being stretched as you lift something up. There is energy available or present in a spring when it is compressed. There is gravitational energy present due to the attraction of masses. In order to build a configuration of objects when gravity is involved you need to put energy into the gravitational field. The amount of energy is related to how far the objects are apart. For our systems of blocks and balls, people and cars on the earth the problem simplifies to h, the height of an object.

 

ASIDE h=0

In terms of calculation the zero point for potential energy is not critical. If you could borrow money from your checking account then you would not be limited by a zero amount as you could keep extracting money it would just be negative or debt. For gravity on the earths surface we can be considering the energy for a ball dropping and make the floor h=0. If we dropped the ball out the window it would fall to a negative value of h but the energy associated with the fall would be positive. In some sense we can keep extracting energy as we go to negative heights and the chosen h=0 is irrelevant in terms of how much energy I have obtained by falling.

This may seem like a tricky point but we do this all the time. We typically measure height wrt the most convenient reference point and not in an absolute sense. In all of the quantities below its really the change or difference in location that is the relevant. The convenient location for your zero point is usually obvious but not required. Establishing the locations of pictures and shelving in a room I could measure the height wrt the floor or the ceiling. As long as the person putting up the pictures and shelves understood the room would be layed out correctly.

SKI AREAS

height from base or lodge

MY HEIGHT

from my feet

DESK

from the floor

HARRISONBURG

from sea level

EARTH

from the sun

SOLAR SYSTEM

from center of milky way

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To continue our model we simply add another checking account. Since this is potential energy we will just open a new account in a different bank.

 

Now that we have identified three types of energy and three locations for money we can address the question of transfer. Energy can be transferred from one form to the other. Your money can be transferred from one location to another. We will simply imagine one ATM machine that does the work. I can take money from my wallet and deposit it or retrieve it from a checking account.

 

Work: Method of energy transfer

work is force through a distance

The formula is complicated by the requirement that in order to do work you need to move in the direction of the force. To encapsulate this idea I suggest you consider throwing and catching a baseball. Here you push the ball in the direction the ball is moving and move your hand along the path of the ball to add energy to the ball and in catching you push opposite the motion along the path. This is all there is to the interpretation of the formula if the force and motion are parallel. If they are perpendicular then no work is done. This is counterintuitive because we experience this differently. Standing and holding an object seems like work and carrying an object seems like work but these actions do not give any energy to the object. If we push something along its motion it speeds up. If the object doesnt move in the direction that we are pushing we do not do work.

 

At this point we will introduce a second method of energy transfer HEAT. We will discuss it in more detail later but identifying it as transfer rather than energy is important so we sill include it in our table

 

 

KE

SPE

GPE

WORK

HEAT

Energy of motion

Spring PE

gravitational

Transfer energy

Energy transfer involving temperature

Money in Wallet

Money in checking account

BANK: spring

Checking

BANK: grav.

ATM moves money from A to B

Different ATM to move money around

 

I like this model because it clearly identifies the difference between work, heat and energy. If you are isolated then you simply add up all the energy and ignore the transfer. The relevant question is how much money do I have. A person can chart, of course, the details and describe the various processes. I deposited $10 in the bank by taking $10 from my wallet. A mass spring system may be isolated and then the energy goes from KEPEKEPE . In the compression the mass does work in the direction of the spring thereby W(mass sp) adds energy to the spring. The spring is pushing opposite the mass so W(sp => mass) takes energy out of the mass and it slows down. So if you want to keep track of the energy and its specific location you will need to look at the transfer or work.

Energy is conserved so whatever is transferred out of one location or form is placed in another location or form. This of course is similar to money at least for ordinary people. We cant make money and it basically moves around without changing, so it is conserved.

 

Just as in the case of money it is often important to isolate certain types of energy and keep track of them. I am very concerned with my total wealth. So in order to keep track of the relevant information I need to have a way to add money to my wealth by taking it from some other location EARN and also to SPEND money that is subtracted from my wealth.

For energy we do not need to introduce a new concept just keep track of the specific types of energy transfer. We define work by external forces. These are forces that act on that add or subtract from our energy. As noted earlier for every force that we exert on an object there is an equal and opposite for (3rd law). So we dont double count. Our spending is another persons earnings. In figuring out how much we have we can ask either how much did I spend or how much did the store earn in figuring my wealth but I dont use both.

 

Positive external work

Negative external work

EARN

SPEND

Something pushes an object in the direction it is moving thereby transferring energy to the object

Now the external force opposes the motion and energy is extracted from the object

 

Nothing new has really been added we are just keeping track of the energy and isolating the system of interest.

 

Equation:

 

Initial Wealth + Earn + Spend = Final Wealth

Initial Wealth = Wallet + checking (spring bank) + checking (gravity bank)

Final Wealth = Wallet + checking (spring bank) + checking (gravity bank)

 

 

 

where W represents all of the work done on the system by external forces

 

For our mass spring system we know that the energy is being removed from the system because it slows down. The air is pushing on the ball as it moves. It always opposes the motion so energy is being continuously removed from the ball. That energy doesnt disappear it ends up as KE and the air moves faster than it was moving initially.

 

Next concepts:

Power Wages (spending rate)

These quantify the rate of energy transfer or the rate of earning or spending

 

 

Wages: $/hour

Wage-hours = PAY

Example wage=$10/hour

6 wage-hours = $60

 

Power: kW = 1000 Watts= 1000J/s

kWh=Energy

Example 5 kWh

1000J/s 5h 3600s/h=18000000 J

 

 

UNITS

Joule (J)=energy =1 kg-m2/s2

calorie 1 cal=4.184 J

Physics cal = energy 1 gm water 1oC

Cal = Food calories= 1000 physics cal

Approximately 1 kWh = 1000 Cal(food)

 

Energy per gram

(see Physics for Future Presidents)

object

Calories

(~Watt-hours)

Joules

 

Versus TNT

bullet (at sound speed- 1000 ft/s)

0.01

40

0.015

battery (auto)

0.03

125

0.05

battery (rechargeable computer)

0.1

400

0.15

battery (alkaline flashlight)

0.15

600

0.23

TNT (the explosive trinitrotoluene)

0.65

2723

1

modern High Explosive (PETN)

1

4200

1.6

chocolate chip cookies

5

21000

8

coal

6

27000

10

butter

7

29000

11

alcohol (ethanol)

6

27000

10

gasoline

10

42000

15

natural gas (methane- CH4)

13

54000

20

hydrogen gas or liquid (H2)

26

110000

40

asteroid or meteor (30 km/sec)

100

450000

165

uranium-235

20 million

82 billion

30 million

Note: many numbers in this table have been rounded off.

For burning reactions (oxidation) that require the addition of oxygen the weight of the oxygen is not included. For a cookie this reduces the C/gm to 2.5. TNT is a self contained reaction no external matter required.

Burning gasoline results in carbon dioxide and water vapor few other gases. No appreciable solid residue to vent.

Adding efficiency gasoline is 80 times better than batteries.

 

 

Transfer

TNT reacts very quickly

Food slow process

Other ingredients

Food, gasoline need air to burn. Oxygen

Residue

Gas burns to gases (motor easy to vent residue)

Efficiency = useful work/total energy

Gas 20%

Electric car 85%

Cost: finding, obtaining, storing, refining

Defining the true cost is often complicated

Miscalculation done to distort value

Hydrogen not available unless you process (NOT source)

Transportation costs

Infrastructure (gas stations, trucks, ships, pipelines)

Hydrogen adds new problems for transportation.

Static vs Mobile use (cars or homes)