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Work & Energy Physics, Chapter 5

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Work Section 5.1

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Definition of Work In Physics, work means more than something that requires physical or mental effort Work is done on an object when a force causes a displacement of the object Work is the product of the force applied to an object and the displacement of the object

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Caution! Work is done only when a force or a component of a force is parallel to a displacement!

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Net Work Done by a Constant Net Force θ F F cos θ d

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Units of Work The SI unit of work is the j jj joule ( J ) Derived from the formula for work The joule is the unit of energy, thus…. Work is a type of energy transfer!!

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Sample Problem A How much work is done on a sled pulled 4.00 m to the right by a force of 75.0 N at an angle of 35.0° above the horizontal? F θ d Fd cosθ

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F FgFg F up θ d How much work was done by F g on the sled? How much work was done by F up on the sled? If the force of kinetic friction was 20.0 N, how much work was done by friction on the sled? FkFk FNFN FyFy FxFx

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The Sign of Work Work is a scalar quantity and can be positive or negative Work is positive when the component force & displacement have the same direction Work is negative when they have opposite directions

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F FgFg F up θ d If the force of kinetic friction was 20.0 N, how much work was done by friction on the sled? W f = F k ∙d = (-20.0 N)(4.00 m) = -80.0 J FkFk

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Graphical Representation of Work Work can be found by analyzing a plot of force and displacement The product F∙d is the area underneath and Fd graph

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Graphical Representation of Work This is particularly useful when force is not constant (which it normally isn’t)

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Energy Section 5.2

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Kinetic Energy Kinetic energy is energy associated with an object in m mm motion KE is a scalar quantity KE depends upon an objects mass and velocity SI unit is the j jj joule

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Sample Problem B What is the speed of a 145 g baseball whose kinetic energy is 131 J? Show that the solution is dimensionally consistent.

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Relationship of Work and Energy Work is a transfer of energy Net work done on an object is equal to the change in kinetic energy of the object

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Proof of W-KE Theorem

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Importance of W-KE Theorem Some problems that can be solved using Newton’s Laws turn out to be very difficult in practice Very often they are solved more simply using a different approach… An energy approach.

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Sample Problem C A 10.0 kg sled is pushed across a frozen pond such that its initial velocity is 2.2 m/s. If the coefficient of kinetic friction between the sled and the ice is 0.10, how far does the sled travel? (Only consider the sled as it is already in motion.) d vivi FkFk FNFN mg

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d FkFk FNFN

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Potential Energy PE is “stored” energy –I–It has the “potential” to do work Energy associated with an object due to its position Gravitational PE g –D–Due to position relative to earth Elastic PE e –D–Due to stretch or compression of a spring

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Two Types of Potential Energy Potential Energy PE g = mgh Gravitational Elastic PE e = ½ kx 2

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Gravitational Potential Energy Gravitational PE is energy related to position PE g = mgh Gravitational PE is relative to position Zero PE is defined by the problem If PE c is zero, then PE A > PE B > PE C

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Elastic Potential Energy PE resulting from the compression or stretching of an elastic material or spring. PE e = ½ kx 2 where… x = distance compressed or stretched k = spring constant Spring constant indicates resistance to stretch.

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5.3 Conservation of Energy Objectives At the end of this section you should be able to 1.Identify situations in which conservation of mechanical energy is valid 2.Recognize the forms that conserved energy can take 3.Solve problems using conservation of mechanical energy

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Conserved Quantities For conserved quantities, the total remains constant, but the form may change Example: one dollar may be changed, but its quantity remains the same. Example: a crystal of salt might be ground to a powder, but the mass remains the same. Mass in conserved

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Mechanical Energy Is conserved in the absence of friction i.e. initial ME equals final ME ME i = ME f If ME = KE + PE Then KE i + PE i = KE f + PE f ½ mv i 2 + mgh i = ½ mv f 2 + mgh f

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Conservation of Mechanical Energy ( A Falling Egg) Time (s) Hght (m) Spd (m/s) PE (J) KE (J) ME (J) 0.001.000.000.740.000.74 0.100.950.980.700.040.74 0.200.802.000.590.150.74 0.300.562.900.410.330.74 0.400.223.900.160.580.74 0.450.004.430.000.74 As a body falls, potential energy is converted to kinetic energy Since ME is conserved (constant)…. ΣPE + KE = ME In the absence of friction & air resistance, this is true for mechanical devices also

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Mechanical Energy Is the sum of KE and all forms of PE in the system ME = ΣKE + ΣPE sigma (Σ ) indicates “the sum of”

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Sample Problem 5E Starting from rest, a child of 25.0 kg slides from a height of 3.0 m down a frictionless slide. What is her velocity at the bottom of the slide? Could solve using kinematic equations, but it is simpler to solve as energy conservation problem. ME i = ME f

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ME may not be conserved In the presence of friction, mechanical energy is not conserved Friction converts some ME into heat energy Total energy is conserved ME i = ME f + heat

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Work-Kinetic Energy Theorem The net work done on an object is equal to the change in kinetic energy of the object W net = ∆KE The work done by friction is equal to the change in mechanical energy W friction = ∆ME

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Power Is the rate of work, the rate at which energy is transferred P = W/∆t Since W = Fd, P = Fd /∆t or P = Fv avg Unit of power = the watt (W) 1 W = 1 J/s 1 hp = 746Whorsepower

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