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Physics 7A – Lecture 4
Winter 2008
Physics 7A – Lecture 4
Winter 2008
Prof. Robin D. Erbacher343 Phy/Geo Bldg
erbacher@physics.ucdavis.edu
Prof. Robin D. Erbacher343 Phy/Geo Bldg
erbacher@physics.ucdavis.edu
• Join this Class Session with your PRS clicker!
• Quiz 2 being graded; Quiz 1 Rubric is posted and grading scale is linked.
• My office hours moved: 10-11:30 am Tuesdays.
• Check Physics 7 website frequently for calendar &Announcements.
• Turn off cell phones and pagers during lecture.
Three New Energy Systems
Three New Energy Systems
EEmovementmovement
(KE)(KE)
EEgravitgravit
yy
EEsprinsprin
gg
Rear shock absorber and spring of
BMW R75/5Motorcycle
• Kinetic energy is simply Emoving.
• 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.
KEtrans = ½ m v2KEtrans = ½ m v2
Baseball
WorkKEKE
SpeedSpeed
€
E total = ΔE1 + ΔE 2 + ΔE 3 + ... = Q + WRemember 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.
KEKESpeedSpeed
Baseball
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!May the Force Be With You!
"an energy field, created by all living things, that surrounds us, penetrates us, and binds the galaxy together."
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
KEKESpeedSpeed
Work
Consider a block being pushed by you on a level surface with no friction:
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
KEKESpeedSpeed
Work
An overall push (or pull!) in against the direction the object
is travelling has the effect of slowing it down.
What’s force got to do with work?
WorkWork 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 = Fparallel ∆x = F|| ∆x
[Joule] = [Newton] [m]=[Nm]
Conservation of Energy says…
∆PEgrav = Work
= Fyou on mass ∆height= mg(hfinal - hinitial)
mm
mm vf=0
Pull
vi=0
Work was done on the mass:Work = F||∆x
Where did the energy go??
∆x PEgrav
HeightWork
What is the indicator of the object change?
Temperature? Phase? Speed?
• Potential energy due to gravity: Eheight. (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 PEgravity.
• The quantitative relationship between PE and height:
(g~10 m/s2 is the acceleration due to gravity on Earth.)
PEgravity = mghPEgravity = mgh
PEgrav
Height
PEgravity = mghPEgravity = mgh
• Gravitational potential energy-system exists for each pair of objects interacting by the gravitational force
• ∆PEgravity 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 PaperKE
SpeedNote: we are neglecting friction
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 4th floor.
Question: How much faster do you need to throw it?
a) 2 times as fastb) Twice as fast• Thrice as fast• 4 times as fast• 16 times as fast
Answer: b, twice as fast!
What is the height of the bowling ball after one full swing?
(a) Same
(b) Higher
(c) Lower
(a) Starting point
(b) When rope is vertical
(c) After reaches point c.
When is the speed of the bowling ball maximum?
ab
c
(a) Starting point
(b) When rope is vertical
(c) After reaches point c.
When is the PEgravity of the bowling ball maximum?
ab
c
PEgravity = KEtranslational
mgh = ½ m v2
Consider a simple pendulum:• At the height (peak) of the amplitude, the object is at rest. Egravity = mgh (define h above the low point)
• At the bottom of the motion, the object is moving quickly, and h=0. Etrans = ½ m v2
Conservation of Energy dictates that:
All of the PE goes into KE, and then back again!
mm
mm 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.
InitialFinal(Still in motion)PEgrav
Height
KESpeed
PEgrav
Height
KESpeed
Final
Initial
(In motion)
PEgrav
Height
KESpeed
Initial
Final (Still in motion)
• 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/s2.
• x: Much easier to stretch a spring a little bit than a lot!
PEspring = ½ kx2PEspring = ½ kx2
x
Clicker Question:
The “equilibrium position” of a mass-spring system is:
A)The “center” of the oscillatory motionB)The position where a spring has no stored PEC)The position where the mass will be at when it eventually stops movingD)The position of maximum kinetic energyE)All of the above
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.
• k is a property of the spring only• PEmass-spring does not depend on mass• PE = 0 arbitrary
PEvertical spring = ½ ky2 +CPEvertical spring = ½ ky2 +C
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 = KEf – KEi = ½ mvf2 – ½ mvi
2
PEgravity = KEtranslational
mgh = ½ m v2)
KEtrans = ½ m v2 KEtrans = ½ m v2
• What are the x-axis, y axis? Units?x axis (independent variable: height)y axis (dependent variable: PEgrav)
• Which quantity (energy) is the easiest to graph?
Etot ? PEgrav? What about KE?
• Where should the origin (0) be placed? Where does it most make sense?
Should the floor be 0m?
Displacement from equilibrium y[+][-]
PEmass-spring
Displacement from equilibrium y[+][-]
direction of force
y
PEmass-spring
Displacement from equilibrium y[+][-]
direction of force
PEmass-spring
Displacement from equilibrium y[+][-]
PEmass-spring
On this side force pushes up
On this side force pushes down
Equilibrium
Forces from potentials point in direction
that (locally) lowers PE
Displacement from equilibrium y[+][-]
PEmass-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
Displacement from equilibrium y[+][-]
PEmass-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
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
Particle Model of Matter
Fermilab BubbleChamber Photo
Atoms in DNA Subatomic particles
Atom 1(anchored)
Atom 2(bonded)
separation
r
PE
Distance between the atoms
Clicker: True or False?
Atoms at large distances from each other attract or repel each other.
separation
r
PE
Distance between the atoms
Clicker: True or False?
It is not possible to squash one atom completely into the other one.
separation
Flattening: atoms have negligible forces at large separation.
r
PE
Distance between the atoms
Repulsive: Atoms push apart as they get too close
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.
Potentialenergy betweenatoms
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.
ro
* ‘Not to scale’
Can you see the forces and energy systems?
= atomic radius
ro
Atoms bound together?
Bonds Formed?
Squeezing?
Bonds breaking?
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
Next Time: Molecular Models
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