Physics 7A – Lecture 4 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg Prof. Robin D. Erbacher 343 Phy/Geo Bldg

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Three New Energy Systems

Examples: Mechanical Phenomena E movement (KE) Egravit y E sprin g Rear shock absorber and spring of BMW R75/5 Motorcycle

Kinetic Energy System (KE) Kinetic energy is simply E moving. For translational energy, the indicator is speed; the faster an object moves, the more KE it has. There is a quantitative relationship between KE and speed. Also, it is proportional to the mass of the object: The direction of motion of the object is unimportant.  KE trans = ½ m  v 2 Baseba ll WorkKESpeed

WorkWork Remember this equation for an open system? You have worked a lot with Q, Heat. Now we introduce Work: Work: A transfer of energy that takes place from a physical system to another physical system due to an interaction that involves a Force. KESpeed Baseba ll Work 1) The pitcher’s hand “pushed” the baseball. 2) The pitcher’s hand exerted force on the baseball. 3) As a result, the baseball started moving (its KE increased).

May the Force Be With You! "an energy field, created by all living things, that surrounds us, penetrates us, and binds the galaxy together."

ForceForce To be more precise, we need the concept of “Force” : “Push” or “Pull” An overall push (or pull!) in the direction the object is travelling has the effect of speeding it up. 1) Block is already moving, you push in same direction: direction of travel direction of Force KESpeed Work Consider a block being pushed by you on a level surface with no friction:

ForceForce To be more precise, we need the concept of “Force” : “Push” or “Pull” Consider a block being pushed by you on a level surface with no friction: 2) Block is already moving, you push in opposite direction: direction of travel direction of Force KESpeed Work An overall push (or pull!) in against the direction the object is travelling has the effect of slowing it down.

WorkWork What’s force got to do with work? Work Transfer of energy into or out of a physical system by a force exerted by another physical system. The change in energy results from an interaction in which an object moves through a distance parallel to the force exerted on it. Work = F parallel ∆x = F || ∆x [Joule] = [Newton] [m]=[Nm]

Conservation of Energy says… ∆PE grav = Work = F you on mass ∆height= mg(h final - h initial ) m m v f =0 Pull v i =0 Work was done on the mass: Work = F || ∆x Where did the energy go?? ∆x PE grav Height Work What is the indicator of the object change? Temperature? Phase? Speed?

Potential Energy System (PE) Potential energy due to gravity: E height. (There are other types of PE, such as PE in a spring, or chemical PE.) For gravitational PE, the indicator is height; a higher object (with respect to something else) has more PE gravity. The quantitative relationship between PE and height: (g~10 m/s 2 is the acceleration due to gravity on Earth.)  PE gravity = mg  h

PE grav Height Gravitational Potential Energy  PE gravity = mg  h Gravitational potential energy-system exists for each pair of objects interacting by the gravitational force ∆PE gravity depends on two quantities: the change in vertical distance that the object moved, and the mass of the object. Usually, we focus on the gravitational potential energy due to the interaction between an object and the Earth. Crumpled Paper KE Speed Note: we are neglecting friction

KE  PE gravity 1) You throw a ball to the height of the first floor window. 2) Now you want to throw a ball to the height of the 4 th floor. Question: How much faster do you need to throw it? a)  2 times as fast b) Twice as fast c) Thrice as fast d) 4 times as fast e) 16 times as fast Answer: b, twice as fast!

Bowling Ball What is the height of the bowling ball after one full swing? (a) Same (b) Higher (c) Lower

Bowling Ball (a) Starting point (b) When rope is vertical (c) After reaches point c. When is the speed of the bowling ball maximum? a b c

Bowling Ball (a) Starting point (b) When rope is vertical (c) After reaches point c. When is the PE gravity of the bowling ball maximum? a b c

Conservation of Energy  PE gravity =  KE translational mg  h = ½ m  v 2 Consider a simple pendulum: At the height (peak) of the amplitude, the object is at rest. E gravity = mgh (define h above the low point) At the bottom of the motion, the object is moving quickly, and h=0. E trans = ½ m   v 2 Conservation of Energy dictates that: All of the PE goes into KE, and then back again!

Work  Kinetic Energy Only? m m v=0 Pull v=0 Mass is pulled part way up a well (like in FNT). This time work is done but there is no change in KE when v=0. Work entering or leaving does NOT automatically mean KE is increasing or decreasing. Similar to how heat entering or leaving does NOT automatically mean the temperature is changing.

Bowling Ball Initial Final (Still in motion) PE grav Height KE Speed

Bowling Ball PE grav Height KE Speed Final Initial (In motion)

Bowling Ball PE grav Height KE Speed Initial Final (Still in motion)

Potential Energy: Springs Springs contain energy when you stretch or compress them. We will use them a lot in Physics 7. The indicator is how much the spring is stretched or compressed,  x, from its equilibrium (rest) state. k is a measure of the “stiffness” of the spring, with units [k] = kg/s 2.  x: Much easier to stretch a spring a little bit than a lot!  PE spring = ½ k  x 2 x

Mass-Spring Systems Clicker Question: The “equilibrium position” of a mass-spring system is: A)The “center” of the oscillatory motion B)The position where a spring has no stored PE C)The position where the mass will be at when it eventually stops moving D)The position of maximum kinetic energy E)All of the above

Mass-Spring Systems Clicker Question: Consider a mass on a vertical spring. At which point is the potential energy the greatest? A)The “equilibrium” position (center of oscillations). B)The highest point the mass goes. C)In between the center and the top position. D)When the kinetic energy is the greatest, too. E)None of the above.

Mass-Spring Systems k is a property of the spring only PE mass-spring does not depend on mass PE = 0 arbitrary  PE vertical spring = ½ k  y 2 +C

Mass-Spring Systems Clicker Question: Is the KE (kinetic energy) of a mass-spring system a function of position? a) No, in this case the potential energy is a function of position. b) The kinetic energy can be treated as a function of position provided the system is open. c) The kinetic energy can always be treated as a function of position in a mass-spring system. d) The kinetic energy can be treated as a function of position provided the system is closed. e) Not enough information is given.

Sometimes from the conservation of energy: We can express KE in terms of position (h, y, etc). KE can never be negative!  KE = KE f – KE i = ½ mv f 2 – ½ mv i 2 Kinetic Energy  PE gravity =  KE translational mg  h = ½ m   v 2 ) KE trans = ½ m v 2

Graphing Energies What are the x-axis, y axis? Units? x axis (independent variable: height) y axis (dependent variable: PE grav ) Which quantity (energy) is the easiest to graph? E tot ? PE grav ? What about KE? Where should the origin (0) be placed? Where does it most make sense? Should the floor be 0m?

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] direction of force yy PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] direction of force PE mass-spring

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring On this side force pushes up On this side force pushes down Equilibrium Forces from potentials point in direction that (locally) lowers PE

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring Equilibrium Potential Energy curve of a spring:  PE = ½ k (  x) 2 W (work) =  PE = -F ║  x Force = -  PE /  x = - k x Putting work into the system increases the energy. Here, work is force through a distance

Potential Energy v. Displacement Displacement from equilibrium y[+][-] PE mass-spring Equilibrium Potential Energy curve of a spring:  PE = ½ k (  x) 2 W (work) =  PE = -F ║  x Force ≈ -  PE /  x ≈ - k x Force is always in direction that decreases PE Force is related to the slope -- NOT the value of PE The steeper the PE vs r graph, the larger the force ~Force

What Does This Have to Do With the Real World? Why does it take more energy to vaporize than to melt? What is Ebond? We will model real atoms of liquids and solids as oscillating masses and springs Particle Model of Matter Three-phase model of matter Energy-interaction model Mass-spring oscillator Particle model of matter  Particle model of bond energy  Particle model of thermal energy Thermodynamics Ideal gas model Statistical model of thermodynamics r

Particle Model of Matter

Normal Matter: Particles Bouncing Around! Fermilab Bubble Chamber Photo Atoms in DNA Subatomic particles

Model Bonded Atoms as Masses on Springs Atom 1 (anchored) Atom 2 (bonded)

Potential Energy Between Two Atoms separation r PE Distance between the atoms Clicker: True or False? Atoms at large distances from each other attract or repel each other.

Potential Energy Between Two Atoms separation r PE Distance between the atoms Clicker: True or False? It is not possible to squash one atom completely into the other one.

Atom-Atom Potential separation Flattening: atoms have negligible forces at large separation. r PE Distance between the atoms Repulsive: Atoms push apart as they get too close

Atom-Atom Potential separation r PE Distance between the atoms The bond is an abstraction: Atoms that don’t have enough energy cannot escape the potential (force), so we treat them as bound until we add enough energy to free them. Potential energy between atoms

Example: Gravitational Potential

Microscopic Picture of Matter Particle: atomic sized object. Attractive forces, Repulsive forces…obvious, but need specifics. (bowl and ball) Center-to-center: here is ‘r’, not surface to surface. (studs) Equilibrium: same as spring, pendulum, ball-in-bowl… Pair-wise Potential Energy: between 2 particles (see above). Single Particle Potential Energy: sum from all interactions with neighbors.

Pair-wise Potential Energy  roro * ‘Not to scale’ Can you see the forces and energy systems?  = atomic radius

 roro Atoms bound together? Bonds Formed? Squeezing? Bonds breaking?

Phases Under the Microscope Liquid: Molecules can move around, but are loosely held together by molecular bonds. Nearly incompressible. Gas: Molecules move freely through space. Compressible. Solid: Rigid, definite shape. Nearly incompressible.

Next Time: Molecular Models