ENERGY ≡ The ability to do WORK

An object that has 100 Joules of ENERGY�has the ABILITY to do 100 Joules of WORK

WORK ≡ Force · Distance

Power is how quickly work is done.�Power is how quickly energy is used.

I can . . .

identify in which “systems” Mechanical Energy is conserved.

explain Conservation of Energy�in terms of Kinetic Energy, Gravitation Potential Energy, and Work.

explain the difference between�relative gravitational potential energy, U_g and

absolute gravitational potential energy, U_G.

CONSERVATION�OF ENERGY

Energy can neither be created nor destroyed;�it can only be transformed from one form to another.

1^st Law of Thermodynamics

CONSERVATION�OF ENERGY

100 Joules of WORK will transform

​

100 Joules of one form of ENERGY into

​

100 Joules of another form of ENERGY.

Work/Energy�Theorem

Positive WORK�INCREASES the Energy of an object

Negative WORK�DECREASES the Energy of an object

http://www.constructionequipmentcompany.com/sitebuildercontent/sitebuilderpictures/wreckrnd.jpg

http://members.shaw.ca/onefishy/engine_room/steam%20turbine%20rotor.02.jpg

http://www.shanerconsultants.com/Power%20Lines%20Sunrise.jpg

Nuclear

Light

Electrical

Mechanical

http://www.spaghetti.it/images/spaghetti-b.jpg

http://wasimsadiq.com/photos/catskills/C08%20Wasim%20by%20Camp%20Fire.jpg

Chemical Energy

Heat Energy

What time of night do you get the coldest ?

Gas

http://us1.webpublications.com.au/static/images/articles/i10/1066_10mg.jpg

Chemical Potential ENERGY

WORK done�by Car

http://www.dot.state.co.us/WolfCreekPass/Images/Rock%20Blast.jpg

http://www.davesfireworks.com/brev_files/dynomite.jpg

Chemical Potential ENERGY

WORK done on rocks

ANFO (Ammonium Nitrate and Fuel Oil)

http://www.vikingrange.com/recipes/recipe_images/banana_pancakes_large.jpg

http://www.woodsfamilyclimbs.com/albums/album16/980800_030_Approaching_the_Diamond_of_Longs_Peak.jpg

Chemical ENERGY

WORK done by Hiker

http://www.industcards.com/cherokee-co.jpg

Chemical Potential ENERGY

WORK done on Steam Turbine

Cherokee Coal Fired Power Plant

http://members.shaw.ca/onefishy/engine_room/steam%20turbine%20rotor.02.jpg

Sound ENERGY

WORK done�on ear

http://www.bierstall.de/images/Hoover%20Dam%202.jpg

Gravitational�Potential ENERGY

http://www.ap.org/westwire/Vegas.jpg

WORK done by lights

Hoover Dam, NV

Las Vegas, NV

El Capitan

Texas Flake

North�American�Wall

The Great Heart

height (distance)

Work done to get the mass there �EQUALS�increase in Potential Energy.

http://3.bp.blogspot.com/_xKPD-D1OYMU/S8KZlOeWtuI/AAAAAAAAACw/BRycTyqPTBk/s1600/crawler-crane-360032.jpg

GRAVITATIONAL POTENTIAL ENERGY�≡ mass · gravity · height

U = m·g·h

UNITS

= Joules

“ENERGY OF POSITION”

KINETIC ENERGY = ½ Mass · Velocity²

K = ½ m·v²

UNITS

= Joules

“ENERGY OF MOTION”

http://www.vikingrange.com/recipes/recipe_images/banana_pancakes_large.jpg

http://www.woodsfamilyclimbs.com/albums/album16/980800_030_Approaching_the_Diamond_of_Longs_Peak.jpg

Chemical ENERGY

WORK done by Hiker

If 10,000 Joules of WORK were done on the backpack,

It would have 10,000 Joules of POTENTIAL ENERGY.

If the backpack is dropped, it would have 10,000 Joules of KINETIC ENERGY just before it hit the snow.

It could do 10,000 Joules of WORK on the snow.

How does the TOTAL KINETIC ENERGY of the balls compare before and after the collision.

Kinetic Energy_Before = Kinetic Energy_After + Heat Energy + Sound Energy

Total Kinetic Energy is LESS After

ENERGY ≡ The ability to do WORK

WORK ≡ Force · Distance

In physics,�Mechanical Energy�is the sum of�Potential Energy and Kinetic Energy.��

�It is the energy associated with the�position and motion of an object.

Where is the velocity the greatest�on this roller coaster?

U_g = 0 J

U_g = 10 J

U_g = 20 J

U_g = 30 J

U_g = 40 J

U_g = 50 J

A

B

C

D

E

K = 35 J

K = 25 J

K = 45 J

K = 15 J

K = 5 J

Where is the velocity the greatest�on this roller coaster?

U = 0 J

U = 10 J

U = 20 J

U = 30 J

U = 40 J

U = 50 J

U = 60 J

U_top = K_bottom

2·g·Δy = v²

v² = 2(9.8)(93.6)

v = 42.8 m/s

v = 95.8 mi/hr

307 ft�93.6 m

How FAST will the coaster be traveling at the bottom?

Steel Dragon - Japan

http://www.rowan.edu/elan/denton/MDL/2000/ccc/day8/revolution_loop_pov.JPG

ΔU_g = Δ K

m∙g∙Δy = ½∙m∙v²

9.8∙ Δy = ½∙8.2²

Δy = 3.4 m

http://history.amusement-parks.com/Revolution/loop.jpg

Find the average frictional force between the snow and the sled.

17.5 m

25.7 m

zero m/s

Mass_{person and sled} = 78.0 kg

ΔU_g = ΔK + W

m·g·Δy = ½·m·v² + f_f·d

78.0·9.8·17.5 = ½·78.0·18.2² + f_f·25.7

f_f = 17.8 N

Systems

Force between car and earth is an internal force.�Potential Energy is transformed into�Kinetic Energy, but Mechanical Energy�stays constant.

Force earth exerts on car is an external force doing positive work increasing�Kinetic Energy and Mechanical Energy.

Potential Energy is irrelevant.

What is the change in Mechanical Energy of each SYSTEM?

ΔU_g = ΔK + W

Decreasing

Increasing

Which situation has a greater change in Mechanical Energy of the Sled System?

Force (N)

Distance (m)

Force (N)

Distance (m)

Hooke’s Law

Work = ½kx·x

.25 m

How fast is the ball traveling here?

m_ball = 175 g

k = 17 N/m

V = 2.5 m/s

=

How is this different?

=

=

.25 m

=

+

How is this different?

=

+

FRICTION

.25 m

How long should the bungee cord be?

½·k·x² = m·g·Δy

½·325·x² = 65·9.8·100.0

k = 325 N/m

m = 65 kg

x = 19.8 m

? = 100 - 19.8 m

? = 80.2 m

Do not try this at home!�The bungee constant, k, changes with length.

x

10 N

5 N

http://www.wolflink.net/~jstorey/porsche/968/js968aa.jpg

½ m·v² = F·d

K = Work

Stopping Distance

30 mph

60 mph

K = ½ m·v²

90 mph

http://www.wolflink.net/~jstorey/porsche/968/js968aa.jpg

Find the KINETIC ENERGY of a 2000 kg car

K = ½ m·v²

10

20

100 kJ

400 kJ

100 kJ

400 kJ

Assume the braking force is 20,000 N.

5 m

20 m

WORK = F · d

http://www.wolflink.net/~jstorey/porsche/968/js968aa.jpg

Find the KINETIC ENERGY of a 2000 kg car

KE = ½ m·v²

10

20

30

40

100 kJ

400 kJ

900 kJ

1,600 kJ

50

2,500 kJ

100 kJ

400 kJ

900 kJ

1,600 kJ

2,500 kJ

Assume the braking force is 20,000 N.

5 m

20 m

45 m

80 m

125 m

WORK = F · d

½·m·v² = μ·m·g·d

How fast was the car traveling when it hit the brakes?

Distance_skidded = 18 m� μ_kinetic= .92

½·m·v² = F_f·d

F_f = μ · F_N

v = 18.0 m/s

v = 40 mph

½·m·v² = μ·F_N·d

v² = 2·μ·g·d

v² = 2·.92·9.8·18

http://www.aviationpics.de/prev/crane%203.jpg

How much POTENTIAL ENERGY does the cylinder have?

30,000 Joules

30,000 = Force · .75

How much WORK can the cylinder do on the “I” beam?

30,000 Joules

30,000 Joules

15 m

How much KINETIC ENERGY will it have just as it hits?

Find the average FORCE on the “I” beam if it got rammed .75 m into the ground.

Force = 40,000 N

Work = Force · Distance

The same 2000 N cylinder is dropped from 15 m.

f = m·a�m = 2000 / 9.8�m = 204.08 kg

How much TIME does it take to fall?

How much VELOCITY does it have when it hits?

v_f = a · t � = 9.8 · 1.749� = 17.14 m/s

How much KINETIC ENERGY does it have when it hits the ground?

What is the cylinder’s MASS?

KE = ½ m·v^2�= ½ 204.1 · 17.14^2�= 30,000 Joules

​

http://home.earthlink.net/~davidon2k/id3.html

Did I lose you somewhere?

If the average resistive force was 60,000 N, and the boat’s mass was 1500 kg, how fast was the boat traveling before it impacted?

Kinetic Energy equals the amount of Work needed to be done in order to stop.

½∙m∙v² = F∙d

v = 15.5 m/s

½∙1500∙v² = 60,000 ∙3

An 80 lb (356.4 N) bow takes an average force of 40 lbs. (178.2 N) to draw it.

How much WORK was done to draw the bow?

= 178.2 N · 0.7 m�= 124.7 Joules

How much POTENTIAL ENERGY does the arrow have?

124.7 Joules

How much KINETIC ENERGY will the arrow have?

124.7 Joules

If the arrow has a mass of .05 kg, how FAST will the arrow travel?

K = ½ m · v² � 124.7 = ½ · .05 · v²� v = 70.6 m/s

0.7 meters

http://library.thinkquest.org/C0125680/media/compound_w-names.gif

http://library.thinkquest.org/C0125680/media/compound_w-names.gif

Never DRY-FIRE�a bow!

Mass_{Bowling Ball} = 8.0 kg

How much Potential Energy does the bowling ball have at TOP OF SWING?

= 8.0 · 9.8 · 0.6� = 47 Joules

How much Kinetic Energy does the bowling ball have AT BOTTOM OF SWING?

K = 47 Joules

How FAST does the bowling ball travel AT BOTTOM OF SWING?

47 = ½ 8.0·v²

v = 3.4 m/s

http://www.kilimanjaroworld.com/Lead%20Climb1.jpg

U_top = K_bottom

http://www.flyingtuna.com/famo/tunadrawn/pages/whit-profile-1.html

Mass_{Bowling Ball} = 8.0 kg

= 8.0 · 9.8 · 0.5� = 39 Joules

38 Joules

38 = 8.0 · 9.8 · h

h = .48 m

How much Potential Energy will the ball have when it returns if it does 1 Joule of work on the air as it goes there and back?

How high will it rise upon return?

http://www.edinburgschools.net/jh/junior%20high%20%20building/jh_building.htm

U_g = zero

RELATIVE Gravitational Potential

ABSOLUTE Gravitational Potential

Find the average height from 1 to 4.

Area = Base x Average Height

Average Height = Area / Base

Find the average height from 1 to 4.

Area = Base x Average Height

Average Height = Area / Base

r_A

r_B

Work = average force · distance

Absolute�Potential�Energy

U_G

Negative because this is how much energy the object lost coming from ∞ to r_b.

-2,000 Joules

-8,000 Joules

ΔU_G = Final - Initial

ΔU_G = -8,000 J – (-2,000 J)

ΔU_G = -6,000 Joules

Object LOST 6,000 Joules

ΔU_G = Final - Initial

ΔU_G = -2,000 J – (-8,000 J)

ΔU_G = +6,000 Joules

Object GAINED 6,000 Joules

How much energy is required to put�a satellite into geosynchronous orbit?

m_e = 5.97219 x 10²⁴ kg

m_satellite = 5,290 kg

r_earth = 6.371 x 10⁶ m

http://antwrp.gsfc.nasa.gov/apod/image/0301/nightlaunch_sts104_big.jpg

http://apod.nasa.gov/apod/ap110525.html

= -3.307558 x 10¹¹ + 5.677709 x 10⁸

= -3.301880 x 10¹¹ Joules

= -4.989680 x 10¹⁰ + 2.494840 x 10¹⁰

= -2.494842 x 10¹⁰ Joules

3.052396 x 10¹¹ Joules

r = 42,232,072.97 m

Kepler’s SECOND LAW OF PLANETARY MOTION

Slowing�Down

Speeding�Up

Kepler’s SECOND LAW OF PLANETARY MOTION

Fastest

Slowest

Kepler’s SECOND LAW OF PLANETARY MOTION

Planets “SWEEP” out equal areas of a sector�in equal times

http://www.physics.fsu.edu/courses/fall98/ast1002/section4/kepler/10_13_27.mov

Force

Distance

Escape Velocity of Earth

The amount of Kinetic Energy an object would have at Earth’s surface is equal to the amount of Potential Energy it had from where it was dropped from. The KE is also equal to the amount of work done in getting it to it’s elevated position.

Escape Velocity of Earth

An object lifted infinitely far above the earth will have an equal amount of Potential Energy as the amount of Work done in lifting it to its position above the earth. This Potential Energy will be converted to Kinetic Energy as the object falls back toward earth. The velocity the object has upon reaching earth is equal to the escape velocity.

zero

I can . . .

identify in which “systems” Mechanical Energy is conserved.

explain Conservation of Energy�in terms of Kinetic Energy, Gravitation Potential Energy, and Work.

explain the difference between�relative gravitational potential energy, U_g and

absolute gravitational potential energy, U_G.