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Chapter 7. Work and Energy Transfer. Section 7.1- Systems and Environments. System- small portion of the universe being studied Can be a single object Can be a collection of objects Environment- everything outside the boundaries (physical or not) of the system

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Chapter 7

Chapter 7

Work and Energy Transfer


Section 7 1 systems and environments
Section 7.1- Systems and Environments

  • System- small portion of the universe being studied

    • Can be a single object

    • Can be a collection of objects

  • Environment- everything outside the boundaries (physical or not) of the system

  • We will generally discuss the conservation of energy of systems rather than individual particles.


7 2 work
7.2- Work

  • Energy- the ability to do work

    • Work is a scalar quantity

      • The product of Force and Displacment

        • Work is only done by forces parallel to the displacement

        • If F |Δr, no work is done

        • At any other angle, only the parallel component of the force does work


7.2

  • Work/Energy have Dimensions of ML2T-2, units = N.m = Joules

  • Work is a form of Energy Transfer

    • Work done on a system (+)

    • Work done by a system (-)

  • Another way of putting it

    • Energy transferred to the system (+)

    • Energy transferred from the system (-)



7.2

  • Quick Quizzes p. 185

  • See Example 7.1 p. 186


7 3 the scalar product
7.3 The Scalar Product

  • Work is a scalar that results from the multiplication of 2 vectors.

    • This is known as…

      • Scalar Product

      • Dot Product

  • Dot Product

    • θ is the angle between A and B


7.3

  • Bcosθ is the projection of B onto A


7.3

  • Work is the dot (scalar) product of the Force vector and displacement vector.


7.3

  • Dot Product Properties-

    • Dot products are commutative

      A . B = B . A

    • Dot products obey distributive laws of mulitplication

      A . ( B + C ) = A . B + A . C


7.3

  • If A is | B then A.B = 0 (cos 90)

  • If A || B then A.B = AB

  • If A anti-|| B then A.B = -AB

  • In Unit vector Notation


  • 7.3

    • Dealing with Unit Vector Coefficients

      Prove this in HW #6

      Quick Quiz p. 187

      Example 7.2, 7.3


    7 4 work and varying force
    7.4 Work and Varying Force

    • is only

      valid when F is constant.

    • For a varying F we

      need to look at very

      small intervals of Δx

      (The smaller the interval, the closer

      Fx becomes to a constant value)


    7.4

    • When Δx is infinitely small, the limit of the sum becomes…

    • Work is Area under an F vs. x curve.



    7.4

    • Work Done by multiple forces

      • The Net work done on an object is equal to the work done by the net force.

      • It can also be found by the sum of the work done by all of the individual forces.


    7.4

    • Common Application- Work done by a spring

      • (Hooke’s Law)

      • x is the position of the attached mass relative to equilibrium

      • k is the spring constant (stiffness)

      • F is always in the opposite direction of x



    7.4

    • Work Done by the Spring

      • Calculate the work done on the blockby the spring in moving from xi = xmax to xf = 0


    7.4

    • Area under the curve

      ½ bh

      ½ xmaxFmax

      ½ xmaxkxmax

      ½ kxmax2

      Work done on block is positive, the spring force is forward while the block moves forward.


    7.4

    Quick Quiz p 192

    Example 7.6


    7 5 kinetic energy
    7.5 Kinetic Energy

    • Work is a way of transferring Energy to a system.

    • Most commonly this energy now “possessed” by the system is energy of motion

    • Kinetic Energy- energy associated with the motion of an object

      Work-Kinetic Energy Theorem


    7.5

    • The Net Work done on an object will equal its change in Kinetic Energy

      • Derivation (see board)

        Quick Quiz p 195

        Examples 7.7, 7.8


    7 6 the non isolated system
    7.6 The Non-Isolated System

    • Non-Isolated System- external forces from the environment

    • Isolated System- no external force (Ch 8)

    • Work-KE Theorem only valid for Non-Isolated


    7.6

    • Internal Energy

      • There are times where we know work is done on an object yet there is no perceivable ΔKE

      • Book Sliding across a table

        • Work is done on the table

        • The table has no change in Kinetic Energy

        • Where did that energy go?

      • The tables temperature increases (due to the work done on it) we call that Eint


    7.6

    • Methods of Energy Transfer

      • Work

      • Mechanical Waves (ex: sound)

      • Heat (increase in average particle KE)

      • Matter Transfer (fuel/convection)

      • Electrical Transmission (charge passing through conductor)

      • Electromagnetic Radiation (Light/UV/IR/radio etc)


    7.6

    • Energy cannot be created nor destroyed, it is conserved

      • It can cross the boundary of our system, but it still exists in the surrounding environment

    • Quick Quizzes p 199


    7 7 involving kinetic friction
    7.7 Involving Kinetic Friction

    • In the case of the book sliding to a stop on the table.

      • The work done ON the book BY friction is responsible for the change of kinetic energy to internal energy.

      • Or with other forces acting on the object


    7.7

    • Or when looking at the book/table system, because there are no outside interactions

    • Therefore the result of a friction force is to transform kinetic energy into an equivalent amount of internal energy


    7.7

    • Quick Quiz p. 201

    • Ex 7.9, 7.11


    7 8 power
    7.8 Power

    • While similar tasks often require the same amount of work, they may not take the same time.

    • Power- the rate of energy transfer

      • The rate at which work is done

      • Refrigerator Example


    7.8

    And so…

    Power is the time rate of change of energy/work

    (derivative)


    7.8

    • Power has dimensions of ML2T-3

      • Units are J/s or Watt

      • Horsepower 1 hp = 746 W

    • Energy described in kWh the energy used for 1 hour at a transfer rate of 1000 W (1 kW, 1000 J/s)

      1 kWh = 1000 J/s x 3600 s = 3.6x106 J


    7.8

    • Quick Quiz p. 204

    • Example 7.12


    7 9 energy and automobiles
    7.9 Energy and Automobiles

    • Modern Internal Combustion engines are very inefficient using less that 15% of the chemical energy stored in gasoline to power the car.

      ~ 67% Lost to heat/sound/emr in the engine

      ~ 10% Lost in friction of the drivetrain

      ~ 4 -10% lost to power Fuel Pumps/Alternator/AC

      Leaves around 13-19% for Kinetic Energy.


    7.9

    • When traveling at constant speeds, the total work done is zero (no change in kinetic energy)

    • The work done by the engine is dissipated by resistive forces

      • Rolling friction

      • Air Resistance ~ v2 (Drag)


    7.9

    • Since drag ~ v2 it is the dominant resistance at high speeds

    • Rolling Friction is dominant at low speeds.


    7.9

    • Examples p. 207


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