Physics of Energy and the Environment - University of...

Physics 161:

Physics of Energy and the Environment

Prof. Raghuveer Parthasarathy

[email protected]

Spring 2010

Physics 161:Physics of Energy & Environment R. Parthasarathy Spring 2010

April 15, 2010

Lecture 6: Announcements

• Reading: Wolfson, Chapter 3

• Homework: Problem Set 3. Due Today April 15

• Homework: Problem Set 4. Due Thurs. April 22. (Posted Fr. morning)

• Office hoursNOTE! RP’s office hours todaymoved to 11.15am‐12.15pm

• Quiz #1: Tuesday, April 20


Last time

• Force, Work, and Energy

• If I have 30,000 J of energy, how much workcan I do?


A. It depends on the distance involvedB. 30,000 JC. 30,000 WD. It depends on the time involved

Equivalence of Work, energy

Last time


• If I have 30,000 J of energy, how much forcecan I apply?



Work = force × distance

Last time


• If I have 30,000 J of energy, how much powercan I apply?



Last time


• If I have 30,000 J of gravitational potential energy, how high can I lift a 1,000 kg mass? (g= 10 m/s2)...


A. 3×108 mB. 30 mC. 3 metersD. It depends on the time involvedE. Not enough information

Egrav = Mgh,so h = Egrav/Mg

= 30,000 J / (1000 kg × 10 m/s2)= (30,000 / 10,000) m [SI units]= 3 m

Energy

• There are many forms of energy

• Energy can be converted from one form to another

• A quick tour (details as needed, later)


Kinetic EnergyKinetic Energy

• Energy associated with motion (e.g. a moving car, a falling leaf...).

• More mass (M) →more kinetic energy

• Greater velocity (v) →more kinetic energy.

• Ekinetic = (½) Mv2 . (i.e. ½×M×v ×v)


Source: istockphoto.com

Potential Energy (1)

Potential Energy

• “Stored energy”E.g. Gravitational potential energy (related to the gravitational field)

E.g. Elastic potential energy


Gravitational Potential Energy

• Gravitational potential energy is proportional to the mass of the object (M), its height (h), and the “acceleration due to gravity” (g) – a measure of the gravitational field.

• Egrav = M g h [remember this]

• At the Earth’s surface, g = 9.8 m/s2. (10 !!)

• SI units:M in kg, g in m/s2, h in m for E to come out in Joules.


Potential and Kinetic Energies

• Consider a pendulum. (A bob of mass Mon a string.)

• Gravitational Potential Energy → Kinetic energy → Gravitational potential energy → ...

• Recall that kinetic energy is associated with motion: Ekinetic = ½M v2.

• Recall that gravitational potential energy is associated with position in a gravitational field (i.e. height): Egrav = M g h.


PendulumWhich of the following statements is true:

When the bob is at the top of its arc...

A. ... its kinetic energy is maximal and its potential energy is minimal.

B. ... its potential energy is maximal and its kinetic energy is minimal.

C. ... its potential and kinetic energies are both maximal.

D. its potential and kinetic energies are both minimal.


PendulumWhich of the following statements is true:

When the bob is at the top of its arc...

B. ... its potential energy is maximal and its kinetic energy is minimal.


• At the top, height is maximal, so the gravitational potential energy is maximal: Egrav = M g h.

• At the top of the arc, the velocity is zero, so the kinetic energy is zero: Ekinetic = ½M v2.

Forms of Energy• Kinetic energy

• Potential energy, esp. gravitational

• Chemical Energy: Energy stored in chemical bonds – released by chemical reactions (e.g. burning gasoline or coal). Also: chemical batteries, food (energy released in the digestive system).



(both)



• Chemical Energy

• Electric Energy: Electricity!Associated with charged objects (electrons)

Chemical energy is fundamentally electrical: rearrangements of electrons in molecules





• Chemical Energy

• Electric Energy

• Electromagnetic Radiation



Light!

Electromagnetic radiation• Light! An electromagnetic wave.


Red: Electric FieldBlue: Magnetic FieldSpeed: The speed of light! (3 × 108 m/s), or 186,000 miles per second

Source: Leiden University, Molecular Physics Group

•Electromagnetic waves carry no mass, just energy. We harness this for...•...Photosynthesis, solar energy, (everything)



• Chemical Energy

• Electric Energy


• Mass Energy: Energy and mass are equivalent: E=mc2.



Mass Energy

• Until the 20th century, it was thought that mass, energy are separate (& separately conserved)

• Deeper insights into physics: Relativity. Consequence: Mass & Energy can convert into one another. (Einstein, 1905). Mass “contains” energy E=mc2, where c = the speed of light.

• (→ Nuclear power)




• Chemical Energy

• Electric Energy


• Mass Energy

• Thermal Energy: Energy of random molecular motion. (Will say more later). Higher temperature →More thermal energy





• Chemical Energy

• Electric Energy


• Mass Energy

• Thermal Energy

• & More


Conservation of Energy

• Energy can be converted from one form to another but cannot be created or destroyed

• “Conservation of Energy”

• A fundamental law of nature! (Never observed to be violated.)

• Not to be confused with “conserving energy” –i.e. trying to “use” less energy. We’ll return to this point later.




• [e.g. pendulum] Kinetic ↔ Potential Energy• “But wait!,” you say. Eventually, the pendulum stops, so clearly energy isn’t conserved; we’ve lost it!

• ??


Friction

• Friction! Our pendulum isn’t just converting itspotential energy to kinetic energy & v.v.

• It’s also transferring energy to the air, my fingers, etc. – largely in the form of thermal energy and other random processes

• If we account for all this energy, it’s conserved –i.e. always the same.


Friction

• But, you might say, that energy lost due to friction is useless to us...

• ... and you’re (mostly) right.

• We need to consider the efficiency of any energy conversion mechanism and

• We need to consider fundamental limitations on the efficiencies of various physical processes. (This will make more sense in a week or so.)




• Simplifies thinking about lots of physical processes. Consider the V‐track (little friction)...

• The ball will rise to a higher position if it starts at


ABC – the same Let’s try...

A B


• Consider the V‐track...• The ball will rise to a higher position if it starts at


ABC – the same

Start: Grav. potl. energy Mgh1

Middle: Kinetic energy. (How much?...)

End: Grav. potl. energy Mgh2.

By conservation of energy, Mgh2must equal Mgh1, so h2 = h1. Nothing else matters!


• Consider the V‐track...


Start: Grav. potl. energy Mgh1

Middle: Kinetic energy. (How much?...)

Must be the same as Mgh1 ! – all this grav. potl. energy got converted to kinetic energy. So if we started out with 10 J of “Mgh”, we in the middle we have 10 J of “½ Mv2”

Another demonstration...


• A ramp


Start: Cart is at height h. Speed = 0. Total energy = gravitational potential energy only = Mgh.End: Cart is at bottom. Speed = v. Total energy = kinetic energy only = (½) Mv2.Conservation of energy requires that

Starting energy = Ending energyMgh = (½) Mv2. (Could solve for v.)

Really?... (Measure!)


• More measurements...


Measure: heights and speeds

00

1.20.10

1.50.14

1.60.18

1.90.24

1.80.20

1.60.16

Speed (m/s)Height (m)

Transportation

• We’ve learned several things about force, energy, power, etc.

• Let’s apply this to gain some insights into transportation – specifically, carsCars consume ≈60% of the energy we use for transportation

• We don’t just want to look up, memorize numbers – we want to understand why things are as they are


Transportation

• Part 1: How much power do we use, per capita, for cars?

• Let’s estimate this, based on things we know.Note: You know lots of things. You can use them!

• Average power = Energy used for driving in one day / 1 day

• Energy used in one day =


miles driven per day miles per gallon

× Energy per gallonNote: this is the only way the units would work out!

(Ask: Arrange things...)

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