Physics%201710%20Section%20004%20Mechanics%20and%20Thermodynamics%20Final%20Review

1
Physics 1710Section 004Mechanics and
ThermodynamicsFinal Review
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2
Physics 1710MWF Session 1 Introduction
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• The Structure of this course

Oscillations
Fluid Mechanics
Waves
Gravitation
Elasticity
Thermodynamics
Applications
Statics
Dynamics
Kinematics
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Physics 1710Chapter 1 Measurement
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• Summary

• Fundamental Dimensions and Units
• Time, measured in seconds
• Length, measured in meters
• Mass, measured in kilograms.
• Prefixes scale units to convenient size. k
  1000, M 1 000 000 c 1/100, m 1/1000, µ
  1/1 000 000
• Density is mass per unit volume. ? m/V kg/m3
  
• Avogadros number is the number of atoms in a
  mole of an element. 6.022 x1023 atom/mole

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Physics 1710Chapter 2 Motion in One
DimensionII
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• The change in the instantaneous velocity is
  equal to the (constant) acceleration multiplied
  by its duration. ?v at
• The displacement is equal to the displacement at
  constant velocity plus one half of the product of
  the acceleration and the square of its duration.
  ?x vinitial t ½ at 2
• The change in the square of the velocity is equal
  to two times the acceleration multiplied by the
  distance traveled during acceleration. ?v 2
  2a ?x
• The acceleration of falling bodies is 9.8 m/s/s
  downward. a - g - 9.8 m/s/s

• Summary

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Physics 1710 Chapter 3 Vectors
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• Summary
• To add vectors, simply add the components
  separately.
• Use the Pythagorean theorem for the magnitude.
• Use trigonometry to get the angle.
• The vector sum will always be equal or less than
  the arithmetic sum of the magnitudes of the
  vectors.

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Physics 1710 Chapter 4 2-D MotionII
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• Summary
• Kinematics in two (or more) dimensions obeys the
  same 1- D equations in each component
  independently.
• rfinal rinitial vinitial t ½ a t 2
• vfinal vinitial a t
• vx,final2 vx,initial 2 2 ax /?x
• vy,final2 vy,initial 2 2 ay /?y
• Projectiles follow a parabola y(x) A Bx
  Cx2

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Physics 1710 Chapter 4 2-D MotionII
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• Summary
• In a moving or accelerating Frame of Reference
• v ' v vframe of reference
• a ' a aframe of reference
• The Centripetal acceleration is
• a - ?2 r or a v 2/ r, toward the
  center.

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Physics 1710 Chapter 5 Laws of MotionII
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• Summary
• Newtons Laws of Motion are
• (1) Acceleration (or deceleration) occurs if and
  only if there is a net external force.
• (2) a F/m Note this is a vector eqn.
• (3) The force exerted by a first object on a
  second is always equal and opposite the the force
  exerted by the second on the first. F12 - F21

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Physics 1710 Chapter 5 Laws of MotionII
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• Summary (contd.)
• Weight is the force of gravity equal to g times
  the mass of the object.
• g 9.80 N/kg
• The force of friction is opposed to the motion
  of a body and proportional to the normal force.
• Free body diagrams are sketches of all the
  forces acting on a body.

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Physics 1710 Chapter 6Circular Motion
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• Summary
• The net force on a body executing circular
  motion is equal to the mass times the centripetal
  acceleration of the body.
• acentripedal v 2/ R toward the center
• The centrifugal force is a fictitious force
  due to a non-inertial frame of reference.

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Physics 1710 Chapter 7Work
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• Summary
• Work is defined to be the distance traveled
  multiplied by the distance over which the force
  acts.
• W ? Fd r
• Joules N m

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Physics 1710 Chapter 78Power Energy
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• Summary
• The Potential Energy is equal to the negative of
  the work done on the system to put it in its
  present state.
• U -? Fd r
• The sum of all energy, potential and kinetic,
  of a system is conserved, in the absence of
  dissipation.
• E U K W
• F - ?U
• P dE/dt

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Physics 1710Chapter 1 Measurement
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• Summary

• F - ?U negative gradient of U.
• The Potential Energy graph is a complete
  description of the dynamics of a system.

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Physics 1710Chapter 10 Rotating Bodies
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• Summary
• Angular displacement is the angle through which a
  body has rotated.
• Instantaneous angular speed is the time rate of
  angular displacement.
• Instantaneous angular acceleration is the time
  rate of change in angular speed.

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Physics 1710Chapter 10 Rotating Bodies
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• Summary (contd)
• The moment of inertia is the measure of the
  (inertial) resistance to angular acceleration and
  equal to the second moment of the mass
  distribution.
• Torque (twist) is the vector product of a
  force and the moment arm.

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Physics 1710Chapter 10 Rotating Bodies
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• Summary
• The moment of inertia I is the measure of the
  (inertial) resistance to angular acceleration and
  equal to the second moment of the mass
  distribution about an axis.

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Physics 1710Chapter 11 Rotating Bodies
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• Summary
• The total Kinetic energy of a rotating system is
  the sum of the rotational energy about the Center
  of Mass and the translational KE of the CM.
• K ½ ICM ? 2 ½ MR 2 ? 2
• t r x F

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Physics 1710Chapter 11 Rotating Bodies
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• Summary

• Angular momentum L is the vector product of the
  moment arm and the linear momentum.
• L r x p
• The net externally applied torque is equal to
  the time rate of change in the angular momentum.
• ? tz d Lz /dt Iz ?

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Physics 1710Chapters 6-10
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• Summary
• Rotary (circular) motion obeys laws that are
  analogous to those of translational motion.
• Linear Momentum is conserved in absence of
  external forces.
• F d p/dt
• Energy is related to the work done or stored
• Work is the cumulative force times distance
  moved.
• Power is the rate of expenditure of work or
  energy.
• Force is the negative of the gradient of the
  potential.

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Physics 1710Chapter 11 Rotating Bodies
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• Summary
• Angular momentum about an axis z is equal to
  the product of the moment of inertia of the body
  about that axis and the angular velocity about z.
• L I ?
• Lz Iz ?
• In the absence of torques, the angular momentum
  is conserved.
• In the presence of torques the angular moment
  will change with time.

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Physics 1710Chapter 11 App E E
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• Summary
• Static equilibrium implies that all forces and
  torques balance.
• The center of mass is often the center of
  gravity.
• The moduli of elasticity characterizes the
  stress-strain relation
• stress modulus x strain
• Stress modulus x strain
• s F/A Y e

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The force of attraction between two bodies with
  mass M and m respectively is proportional to the
  product of their masses and inversely
  proportional to the distance between their
  centers squared.
• F - G M m/ r 2
• The proportionality constant in the Universal
  Law of Gravitation G is equal to 6.673 x 10 11 N
  m2 /kg2 .

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The gravitational force constant g is equal to
• G M/(Rh) 2, R is the radius of the planet.
• Keplers Laws
• The orbits of the planets are ellipses.
• The areal velocity of a planet is constant.
• The cube of the radius of a planets orbit
• is proportional to the square of the period.
• The gravitation field is the force divided by
  the mass.
• g Fg / m

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The force of attraction between two bodies with
  mass M and m respectively is proportional to the
  product of their masses and inversely
  proportional to the distance between their
  centers squared.
• F - G M m/ r 2
• The proportionality constant in the Universal
  Law of Gravitation G is equal to 6.673 x 10 11 N
  m2 /kg2 .

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The gravitation potential energy for a point
  mass is proportional to the product of the masses
  and inversely proportional to the distance
  between their centers
• U GMm / r
• The escape velocity is the minimum speed a
  projectile must have at the surface of a planet
  to escape the gravitational field.
• vescape v 2GM/R
• Total Energy E is conserved for two body
  geavitational problem bodies are bound for E 0
• E L2/2mr 2 GMm/r

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Physics 1710Chapter 14 Fluid Dynamics
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• Summary
• Pressure is the force per unit area. P F/A
• Unit of pressure Pacal N/m2
• The hydrostatic pressure is P Po ?gh
• Archimedes Principle Fbouyant ?fluid g V
• Equation of Continuity A1v1 A2v2
• Bernoullis Equation P ½ ?v2 ?gy
  constant.

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Physics 1710Chapter 15 SHO
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• Summary
• Simple Harmonic Motion is sinusoidal. x
  Xo cos(?t f)
• The period is the reciprocal of the
  frequency. T 1/ f
• For a mass m on a spring of spring constant k,
  the period T 2pv(m/k)
• For Damped SHO, the frequency is decreased and
  the amplitude decays exponentially.
• x Xo e ½ (b/m)t cos(?t f)with ? vk/m ½
  b/m

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Physics 1710Chapter 15 SHO
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• Summary
• For a driven SHO the amplitude is a maximum when
  the drive frequency is equal to the natural
  frequency a condition known as resonance.
• A simple pendulum oscillates at a frequency of
  f (1/2p) v(g/L)
• A physical pendulum oscillates at a frequency of
  f (1/2p) v(mgL/I)

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Physics 1710Chapter 16 Waves
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• Summary
• A traveling wave has the form y(x,t) Y
  sin(kx ?t), with k 2p/?, k wave number,
  ? wavelength ? 2p f 2p/ T as previously
  defined
• d 2y/dx 2 (1/v 2) d 2y/dt 2 is the linear wave
  equation.
• ? f v, the phase velocity.
• For a longitudinal wave on a string v v(T/µ).
  T tension, µ dm/dx linear mass density
• The time averaged power transmitted on a string
  is P ½ µ ?2A2v

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Physics 1710Chapter 17 Sound
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• Summary
• Sound is a longitudinal pressure/displacement
• V vB/?, the phase velocity is equal to the
  square root of the ratio of the bulk modulus to
  the density.
• The Doppler effect is a shift in frequency due
  to the relative motion of the source and observer
  of a sound.

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Physics 1710Chapter 16 Waves
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• Summary
• A traveling wave has the form y(x,t) Y
  sin(kx ?t), with k 2p/?, k wave number,
  ? wavelength ? 2p f 2p/ T as previously
  defined
• d 2y/dx 2 (1/v 2) d 2y/dt 2 is the linear wave
  equation.
• ? f v, the phase velocity.
• For a longitudinal wave on a string v v(T/µ).
  T tension, µ dm/dx linear mass density
• The time averaged power transmitted on a string
  is P ½ µ ?2A2v

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Physics 1710Chapter 18 Chapter 18 Superposition
and Standing Waves
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• Summary
• The propagation of waves is characterized by
• Reflection the rebound of the wave.
• Refraction the bending of a waves
  direction due to a velocity gradient
• Diffraction the bending of a wave around
  obstacles.
• Interference the combination of two or more
  waves in space.
• Beats the combination of two waves in time.

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Physics 1710Chapter 18 Chapter 18 Superposition
and Standing Waves
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• Summary
• Angle of incidence angle of reflection
  ? i ? r
• sin ? 1 /v1 sin ? 2 / v2
• fave ( f1 f2 )/2 fbeat ( f1 - f2 )
• fn n /(2L) v(T/µ)
• A (Fext /m)/ ?0 2 - ?2

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Physics 1710Chapter 19 Temperature
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• Summary
• Temperature is a measure of the average kinetic
  energy of a system of particles.
• Thermal Equilibrium means that two bodies are at
  the same temperature.
• The Zeroth Law of Thermodynamics states that
  if system A and B are n thermal equilibrium with
  system C, then A and B are in thermal Equilibrium
  with each other.

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Physics 1710Chapter 19 Temperature
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• Kelvin is a unit of temperature where one degree
  K is 1/279.16 of the temperature of the triple
  point of water (near freezing).
• TC (100/180) (TF 32 F)
• TF (180/100) TC 32 F
• ?L/L a?T
• PV n R T N kT

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Physics 1710 Chapter 20 Heat 1st Law of Thermo
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• Summary
• The internal energy is the total average energy
  of the atoms of an object.
• Heat is the change in internal energy.
• The change in temperature is proportional to the
  change in internal energy (heat flow) when there
  is no change of phase and the system does no
  work.
• The first law of thermodynamics states
• ?E ?Q - W

37
Physics 1710 Chapter 21 Kinetic theory of Gases

• Summary
• The Ideal Gas Law results from the cumulative
  action of atoms or molecules.
• The average kinetic energy of the atoms or
  molecules of an ideal gas is equal to 3/2 kT.
• ½ mltv2gt 3/2 kT
• Energy average distributes equally (is
  equipartitioned) into all available states.
• Each degree of freedom contributes 1/2 kT to the
  energy of a system.

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Physics 1710 Chapter 21 Kinetic theory of Gases

• Summary (contd.)
• ? CP / CV
• PV ? constant
• B ? P
• The distribution of particles among available
  energy states obeys the Boltzmann distribution
  law.
• nV no e E/kT

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Physics 1710Chapter 22 Heat Engines etc

• Summary
• The work done by a heat engine is equal to the
  difference in the heat absorbed at the high
  temperature and expelled at the low.
• ?W ?Qh ?Qc
• The thermal efficiency is the work done divided
  by the heat absorbed.
• e 1 - ?Qc / ?Qh

40
Physics 1710Chapter 22 Heat Engines etc

• Summary
• Kelvin-Planck form of 2 nd Law of Thermo It is
  impossible to construct a heat engine that,
  operating in a cycle, produces no effect other
  than the absorption of energy from a reservoir
  and the performance of an equal amount of work.
• Clausius Form of 2 nd Law of Thermo It is
  impossible to construct a cyclical machine whose
  sole effect is the continuous transfer of energy
  from one object to another at a higher
  temperature without the input of work.

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Physics 1710Chapter 22 Heat Engines etc
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• Summary
• The maximum efficiency is obtained via a Carnot
  cycle and is equal to the temperature difference
  divided by the high temperature.
• eCarnot 1 - Tc / Th
• Entropy S is a measure of the disorder of a
  system.
• ?S ?dQ/T
• S k ln N