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WARM UPWARM UP

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)1) 1)

Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)1) 1)

Warm UpWarm Up2) A block is pushed along a horizontal, frictionless 2) A block is pushed along a horizontal, frictionless

surface, with a horizontal Force that varies as a surface, with a horizontal Force that varies as a function of time as shown in the graph here. The function of time as shown in the graph here. The mass of the bloc is 3kg. If the block was at rest at mass of the bloc is 3kg. If the block was at rest at time t=0, what is the speed of the block at time t=3? time t=0, what is the speed of the block at time t=3?

Warm up 2Warm up 2

Warm UpWarm Up3) Three blocks of mass 3) Three blocks of mass m, 2m, m, 2m, and and 3m 3m are placed are placed

adjacent to each other on a frictionless horizontal adjacent to each other on a frictionless horizontal surface as shown above. A constant force of surface as shown above. A constant force of magnitude F is applied to the right. Which of the magnitude F is applied to the right. Which of the following statements is true?following statements is true?

Warm UpWarm Up

Warm UpWarm Up4) Two masses, M>m, are connected by a light string 4) Two masses, M>m, are connected by a light string

hanging over a pulley of negligible mass. When the hanging over a pulley of negligible mass. When the masses are released from rest, the magnitude of the masses are released from rest, the magnitude of the acceleration of the masses is?acceleration of the masses is?

Warm UpWarm Up5) A mass of 2.0kg is attached to the end of a light cord 5) A mass of 2.0kg is attached to the end of a light cord

to make a pendulum 5.0m in length. The mass is to make a pendulum 5.0m in length. The mass is raised to an angle of 53 relative to the vertical, as raised to an angle of 53 relative to the vertical, as shown, and released. The speed of the mass at the shown, and released. The speed of the mass at the bottom of the swing is:bottom of the swing is:

Warm UpWarm Up6) A cannon is mounted on a cart, and 6) A cannon is mounted on a cart, and

carrying a cannonball. The total carrying a cannonball. The total mass of the cart, cannon, and ball is mass of the cart, cannon, and ball is MM, and the cart is rolling with no , and the cart is rolling with no friction at a velocity friction at a velocity vv in the positive in the positive direction as shown above. The ball, direction as shown above. The ball, of mass of mass mm, , is fired with a velocity is fired with a velocity vvballball in the positive x direction. What is in the positive x direction. What is the velocity of the cart and cannon the velocity of the cart and cannon after the ball is fired?after the ball is fired?

Warm UpWarm Up6)6)

Warm UpWarm Up

Awesome Gas VideoAwesome Gas Video

NO WARM UP!NO WARM UP!

Warm UpWarm Up7) A student lies on a rigid platform of negligible mass, which is in turn 7) A student lies on a rigid platform of negligible mass, which is in turn

placed upon two spring scales as shown above. The left scale at placed upon two spring scales as shown above. The left scale at position 0 reads 200N, and the scale on the right at position L, reads position 0 reads 200N, and the scale on the right at position L, reads 300N. Find the value of X in terms of L. 300N. Find the value of X in terms of L.

a. X = 1/2 La. X = 1/2 Lb. X = 2/5 Lb. X = 2/5 Lc. X = 3/5 Lc. X = 3/5 Ld. X = 3/4 Ld. X = 3/4 Le. X = 4/5 Le. X = 4/5 L

PIVOT POINT

Warm UpWarm Up88))

Warm UpWarm Up88))

Warm UpWarm Up99) A pendulum driven clock, ) A pendulum driven clock,

located on earth, is set into located on earth, is set into motion by releasing its 10m motion by releasing its 10m long simple pendulum from a long simple pendulum from a maximum angle of less than maximum angle of less than 10° relative to the vertical. At 10° relative to the vertical. At what approximate time what approximate time t t will will the pendulum have fallen to a the pendulum have fallen to a perfectly vertical orientation? perfectly vertical orientation? (Use 10 for g)(Use 10 for g)

Warm UpWarm Up

Warm UpWarm Up1010) By visual ) By visual

inspection, order the inspection, order the PV diagrams shown PV diagrams shown from the most from the most negative work done negative work done on the system to the on the system to the most positive work most positive work done on the system.done on the system.

A.A. a,b,c,da,b,c,dB.B. a,c,b,da,c,b,dC.C. d,b,c,ad,b,c,aD.D. d,a,c,bd,a,c,b

LessonLesson

AnnouncementsAnnouncementsPass Back Fluids Quiz:

Thermo Quiz Friday!

What are important quantities in What are important quantities in thermodynamics?thermodynamics?

PressurePressure Atoms colliding w/ wall of a container Atoms colliding w/ wall of a container

TemperatureTemperature How fast atoms move How fast atoms move

VolumeVolume How much space atoms “need” to move freely How much space atoms “need” to move freely

Number of molecules Number of molecules Really big numbersReally big numbers

Kinetic Theory of Gases Kinetic Theory of Gases AssumptionsAssumptions for an IDEAL GASfor an IDEAL GAS

1)1) Atom are Atom are bouncy:bouncy: Elastic collisions between atomsElastic collisions between atoms

2)2) Atoms are Atoms are spread outspread out: : Far away unless collidingFar away unless colliding

3)3) Atoms are Atoms are randomrandom: : No preferred direction of No preferred direction of motion (means pressure is equal motion (means pressure is equal everywhere in a containereverywhere in a container

Calculation – Units to useCalculation – Units to use PressurePressure ALWAYS ALWAYS Pascals (N/mPascals (N/m22 ) )

TemperatureTemperature ALWAYS ALWAYS KelvinKelvin ( (273 + 273 + ooC)C)

VolumeVolume ALWAYS ALWAYS mm33 (Liters/1000)(Liters/1000)

Number of molecules Number of molecules moles or moleculesmoles or moleculesMoles = Molecules/6.02E23Moles = Molecules/6.02E23

R = 8.31J/molKR = 8.31J/molK KKbb = 1.38 E-23 J/K = 1.38 E-23 J/K

Equation’s so farEquation’s so far1.1. PV = nRTPV = nRT2.2. PV = NkPV = NkbbTT

3.3. PP1 1 VV1 1 / T/ T11 = P = P2 2 VV2 2 / T/ T22

4.4.

5.5. M is molar mass M is molar mass

Energy of a GasEnergy of a Gas

1.1. ΔU = Q + WΔU = Q + W2.2. U = 3/2 nRTU = 3/2 nRT3.3. U = 3/2 PVU = 3/2 PV

Energy Type (+) (-)U = Internal

energy Temp INCREASE TEMP DECREASE

Q = HEAT HEAD ADDED HEAT REMOVED

W = Work GAS CONTRACTS (WORK ON)

GAS EXPANDS (WORK BY)

Gas ProcessGas Process The The thermodynamic statethermodynamic state of a gas is of a gas is

defined by pressure, volume, and defined by pressure, volume, and temperature.temperature.

A “gas process” describes how gas gets A “gas process” describes how gas gets from one state to another state.from one state to another state.

T1

Isothermal ProcessIsothermal Process(constant temperature)(constant temperature)

P

VT = 0 (constant T)

Hayon: Pull plunger up from halfway (slowly)

Isobaric ProcessIsobaric Process(constant pressure)(constant pressure)

P

VP = 0 (constant P)

Isobaric Expansion

Isobaric Contraction

Hayon: Heat up the tank while allowing plunger to move

Isometric ProcessIsometric Process(constant volume)(constant volume)

P

VV = 0 (constant V)

Hayon: Push to the top and then heat up or push to the bottom and then cool down

NO WORK POSSIBLE!!

Adiabatic processAdiabatic process(PERFECTLY insulated)(PERFECTLY insulated)

P

V

T

isotherm

adiabat

Q = 0 (no heat enters or leaves)

NO HEAT IS NO HEAT IS TRANSFEREDTRANSFERED

ΔU = W

Example ProblemExample Problem0.25 moles of a gas are kept at 1150K. The gas undergoes adiabatic expansion, reaching a final temperature of 400K. How much work was done on or by the gas?

U = 3/2 nRT

Using PV DiagramsUsing PV Diagrams

WORK = Area under a PV Diagram WORK = Area under a PV Diagram

P

V

100kpa

200kpa

300m2250m2

Hayon: Test (remember area) and don’t use 1 way valve

(+) = Contract(+) = Contract(-) = Expand(-) = Expand

Free Response ProblemsFree Response Problems FR #1 as an ExampleFR #1 as an Example

Web Assign: Thermo Assignment #2Web Assign: Thermo Assignment #2

Then skip #2 and go to the backThen skip #2 and go to the back