the nature of energy. energy energy the ability to cause change. the ability to cause change. scalar...
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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
Forms of EnergyForms of Energy
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.
Forms of EnergyForms of Energy
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.
Forms of EnergyForms of Energy
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
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Kinetic EnergyKinetic Energy
Mass = 10 kg
0200040006000800010000120001400016000
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Velocity (m/s)
Kin
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Kinetic EnergyKinetic Energy
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
Kinetic EnergyKinetic Energy
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
Mechanical EnergyMechanical Energy
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
Mechanical EnergyMechanical Energy
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
Mechanical EnergyMechanical Energy
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
UUgg = 38.1 million Joules = 38.1 million Joules
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?
UUgg = 38.1 million Joules = 38.1 million Joules
K = 36.1 million JoulesK = 36.1 million Joules
Mechanical EnergyMechanical Energy
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.
Elastic Potential EnergyElastic Potential Energy
k = 50 N/m
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Stretch (cm)
Sp
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g F
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F =
kx
Ue = ½ kx2
Elastic Potential EnergyElastic Potential Energy
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