the nature of energy. energy energy the ability to cause change. the ability to cause change. scalar...

The Nature of EnergyThe Nature of Energy

The Nature of EnergyThe Nature of EnergyEnergyEnergy

The ability to cause change.The ability to cause change.Scalar quantity.Scalar quantity.

Does NOT depend on direction.Does NOT depend on direction.Unit: kg*mUnit: kg*m22/s/s22

= N*m= N*m= Joule (J)= Joule (J)

All energy can be broadly classified All energy can be broadly classified as as potentialpotential or or kinetickinetic..Potential energyPotential energy – energy in storage. – energy in storage.Kinetic energyKinetic energy – energy in motion. – energy in motion.

Forms of EnergyForms of Energy

Energy can change Energy can change from one form to from one form to another.another. Remember “I SCREAM”Remember “I SCREAM”

I = InternalI = InternalS = SoundS = SoundC = ChemicalC = ChemicalR = RadiantR = RadiantE = ElectricalE = ElectricalA = AtomicA = AtomicM = MechanicalM = Mechanical


Internal EnergyInternal Energyenergy assoc. with particles in a energy assoc. with particles in a

substance.substance.temperature and phase are assoc. w/ temperature and phase are assoc. w/

internal energy.internal energy.Sound EnergySound Energy

released when an object vibrates.released when an object vibrates.needs a medium in which to travel.needs a medium in which to travel.


Chemical EnergyChemical EnergyEnergy stored in chemical bonds.Energy stored in chemical bonds.Batteries, gasoline, and food all store Batteries, gasoline, and food all store

chemical potential energy.chemical potential energy.Radiant EnergyRadiant Energy

Energy carried by light.Energy carried by light.Electrical EnergyElectrical Energy

Energy assoc. w/ the movement of Energy assoc. w/ the movement of electrons through a substance.electrons through a substance.


Atomic EnergyAtomic EnergyEnergy stored in the nucleus of an atom Energy stored in the nucleus of an atom

(nuclear energy).(nuclear energy).Mechanical EnergyMechanical Energy

Kinetic = energy assoc. with a moving Kinetic = energy assoc. with a moving object.object.

Potential = energy assoc. with an object Potential = energy assoc. with an object b/c of its position or deformation.b/c of its position or deformation.

Kinetic Energy (K)Kinetic Energy (K)

Energy of a moving object.Energy of a moving object.K = ½ mvK = ½ mv22

Kinetic EnergyKinetic Energy

Velocity = 5 m/s

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Mass (kg)

Kin

etic

En

erg

y (J

)


Mass = 10 kg

0200040006000800010000120001400016000

0 10 20 30 40 50 60

Velocity (m/s)

Kin

etic

En

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y (J

)


What is the kinetic energy of a 1500.-What is the kinetic energy of a 1500.-kg vehicle moving at 20.0 m/s?kg vehicle moving at 20.0 m/s?K = ½ mvK = ½ mv22

K = ½ (1500. kg)(20.0 m/s)K = ½ (1500. kg)(20.0 m/s)22

K = ½ (1500. kg)(400. mK = ½ (1500. kg)(400. m22/s/s22))K = 3.00x10K = 3.00x1055 J J


A .30-06 bullet has a mass of 11.2 A .30-06 bullet has a mass of 11.2 grams and a kinetic energy of 3840 J. grams and a kinetic energy of 3840 J. What is the speed of the bullet? What is the speed of the bullet?First convert grams to kilograms:First convert grams to kilograms:

11.2 g = 0.0112 kg11.2 g = 0.0112 kgK = ½ mvK = ½ mv22

3840 J = ½ (0.0112 kg)v3840 J = ½ (0.0112 kg)v22

686 000 m686 000 m22/s/s22 = v = v22

v = 828 m/sv = 828 m/s

Gravitational Potential EnergyGravitational Potential Energy

UUgg – Energy stored by an object – Energy stored by an object because of its position in a because of its position in a gravitational field.gravitational field.UUgg = mgh = mgh

m = mass (kg)m = mass (kg)g = gravity (m/sg = gravity (m/s22))h = height (m)h = height (m)

Must always be measured relative to Must always be measured relative to some point.some point.

Gravitational Potential EnergyGravitational Potential Energy

As an object falls, UAs an object falls, Ugg turns to K. turns to K.UUgg + K = Mechanical Energy + K = Mechanical Energy

In a world w/o friction, Mech. Energy is In a world w/o friction, Mech. Energy is constant.constant.K + UK + Ugg = constant for all falling bodies = constant for all falling bodies

In the real world, friction robs moving In the real world, friction robs moving objects of energyobjects of energyMech. Energy of a free-falling body in Mech. Energy of a free-falling body in

Earth’s atmosphere constantly Earth’s atmosphere constantly diminishes.diminishes.

Mechanical EnergyMechanical Energy

Ideal WorldIdeal WorldUUg,og,o K = 0K = 0

K = UK = Ug,og,o

Real WorldReal WorldUUg,og,o K = 0K = 0

K < UK < UG,oG,o


A 2.00-kg stone is dropped from a A 2.00-kg stone is dropped from a height of 50.0 meters. What is its height of 50.0 meters. What is its velocity when it reaches the ground? velocity when it reaches the ground? (Ignore air resistance)(Ignore air resistance)In the absence of drag, its K upon In the absence of drag, its K upon

reaching the ground = its starting Ureaching the ground = its starting Ugg..

UUgg = mgh = (2.00 kg)(9.81 m/s = mgh = (2.00 kg)(9.81 m/s22)(50.0 m))(50.0 m)

UUgg = 981 J = 981 JK = 981 JK = 981 J


A 2.00-kg stone is dropped from a A 2.00-kg stone is dropped from a height of 50.0 meters. What is its height of 50.0 meters. What is its velocity when it reaches the ground? velocity when it reaches the ground? (Ignore air resistance)(Ignore air resistance)K = 981 JK = 981 J981 J = ½ (2.00 kg)v981 J = ½ (2.00 kg)v22

981 J = (1.00 kg)v981 J = (1.00 kg)v22

981 m981 m22/s/s22 = v = v22

v = 31.3 m/sv = 31.3 m/s


The Titan roller coaster at Six Flags Over Texas The Titan roller coaster at Six Flags Over Texas features a drop of 255 feet (77.7 meters) and features a drop of 255 feet (77.7 meters) and has a top speed of 85 mph (38.0 m/s).has a top speed of 85 mph (38.0 m/s).

Mechanical EnergyMechanical Energy If the mass of a roller coaster train is 5000. If the mass of a roller coaster train is 5000.

kg, what is the GPE of the train at the top of kg, what is the GPE of the train at the top of the first hill (relative to the bottom of the hill)?the first hill (relative to the bottom of the hill)? GPE = mgh = (5000. kg)(9.81 m/sGPE = mgh = (5000. kg)(9.81 m/s22)(77.7 m))(77.7 m) GPE = 3.81x10GPE = 3.81x1077 J J

UUgg = 38.1 million Joules = 38.1 million Joules

Mechanical EnergyMechanical Energy The 5000.-kg train is moving at 38.0 m/s at the The 5000.-kg train is moving at 38.0 m/s at the

bottom of the first hill. What is the car’s KE?bottom of the first hill. What is the car’s KE? KE = ½ mvKE = ½ mv22

KE = ½ (5000. kg)(38.0 m/s)KE = ½ (5000. kg)(38.0 m/s)22

KE = 3.61x10KE = 3.61x1077 J J


K = 36.1 million JoulesK = 36.1 million Joules

Mechanical EnergyMechanical Energy How much of the car’s Mech. Energy was How much of the car’s Mech. Energy was

converted to other forms in the first drop?converted to other forms in the first drop? 3.81x103.81x1077 J – 3.61x10 J – 3.61x1077 J = 2.0x10 J = 2.0x1066 J J

What kinds of energy might the mechanical What kinds of energy might the mechanical energy have been converted to?energy have been converted to?


K = 36.1 million JoulesK = 36.1 million Joules


Imagine a 50.0-kg crate perched on Imagine a 50.0-kg crate perched on shelf 2.0 meters above the ground.shelf 2.0 meters above the ground.Now imagine the same crate on the Now imagine the same crate on the

same shelf, except now it’s on the Moon.same shelf, except now it’s on the Moon.Does the crate have more, the same, Does the crate have more, the same,

or less Uor less Ugg on the Moon than it has on on the Moon than it has on Earth?Earth?It has less because It has less because gg is smaller on the is smaller on the

Moon than it is on Earth.Moon than it is on Earth.

Elastic Potential EnergyElastic Potential Energy

UUee = energy stored by an object = energy stored by an object when it is deformed.when it is deformed.Most common example: springsMost common example: springs

UUee = ½ kx = ½ kx22

k = spring constant (N/m)k = spring constant (N/m)x = stretch (m)x = stretch (m)

For You Calculus PeopleFor You Calculus People

Recall that FRecall that Fspringspring = kx. = kx. If f(x) = ½ kxIf f(x) = ½ kx22, then f’(x) = kx, then f’(x) = kx

In other words, the force needed to In other words, the force needed to stretch a spring to a distance stretch a spring to a distance xx is the is the first derivative of the potential energy first derivative of the potential energy stored in the spring when it is stretched stored in the spring when it is stretched to to xx..

Also, the potential energy is the integral Also, the potential energy is the integral of a force-vs-stretch graph.of a force-vs-stretch graph.


k = 50 N/m

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g F

orc

e (N

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F =

kx

Ue = ½ kx2


How much force is required to How much force is required to stretch a 50.0-N/m spring 25.0 cm? stretch a 50.0-N/m spring 25.0 cm? How much potential energy is stored How much potential energy is stored in the stretched spring?in the stretched spring?FFss = kx = kx

FFss = (50.0 N/m)(0.250 m) = 12.5 N = (50.0 N/m)(0.250 m) = 12.5 N

UUee = ½ kx = ½ kx22

UUee = ½ (50.0 N/m)(0.250 m) = ½ (50.0 N/m)(0.250 m)22 = 1.56 J = 1.56 J

the nature of energy. energy energy the ability to cause change. the ability to cause change. scalar...

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