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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 1 Puzzler: A monkey hangs on a rope. The rope goes up over a pulley, and on the other end is a weight, which exactly balances the monkey. Everything is balanced, and is initially stationary. (As usual, friction is negligible, and so are mass of rope and pulley.) The monkey tries to climb the rope. What happens? 1)Only monkey rises 2)Monkey & weight both rise, but monkey faster 3)Monkey & weight both rise together 4)Monkey & weight both rise, but weight faster 5)Only weight rises http://activityworkshop.net/puzzlesgames/monkey/

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 2 ANNOUNCEMENTS

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 3 1 of 3 Carts A and B move on frictionless tracks. Cart A has a thruster directed along the track applying a force F. Cart B has its thruster applying force F directed at 60 deg with respect to the track. Both are released and allowed to travel 2 m. During their flights, the work done on B by the thruster was 1.Zero. 2.Less than half the work done on A. 3.Half the work done on A. 4.Equal to the work done on A. F F A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 4 2 of 3 Body A is dropped from rest into vertical free fall. Body B is released from rest down a frictionless incline. The kinetic energy gained by body B is 1.Greater than that gained by A. 2.Equal to that gained by A. 3.Less than that gained by A. 4.Zero. A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 5 3 of 3 Body A is released from rest down a frictionless incline. Body B is released from rest to travel down a frictionless curvy track. It is assumed that B stays on the track and reaches the bottom. The kinetic energy gained by body B is 1.Greater than that gained by A. 2.Equal to that gained by A. 3.Less than that gained by A. 4.Zero. A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 6 ANNOUNCEMENTS

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 Deriving the Work-Energy Theorem from Newton’s Second Law of Motion Newton’s 2 nd Law of Motion “path integrating” Newton’s 2 nd Law x path of motion y dr A little displacement along the path of motion The “dot” product: Multiply the magnitude of one vector times the component of the other that lies along the first: 7

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 Deriving the Work-Energy Theorem from Newton’s Second Law of Motion Newton’s 2 nd Law of Motion “path integrating” Newton’s 2 nd Law Take a little displacement, multiply by the component of the net force acting along the path, and add all those up along the path of motion. This is called the “net work:” = This is called the “Work – Energy Theorem” 8

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 The Work of a Force Because of … It is meaningful to speak of the “work of a force:” 9

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 Compare and Contrast Two Methods of Dynamical Analysis vector equationscalar equation snapshot in time (free body diagram) through-time analysis (from t 1 to t 2 ) units of Nunits of J solve for forces, acceleration solve for average net force, speed 10

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 Must be careful when applying work-energy principles to non- particulate or non-rigid bodies: Both particles and rigid bodies are structureless, ideal entities, not thought of as being composed of any smaller interacting structures. A particle or rigid body has no “internal degrees of freedom” in which to store internal energy (thermal energy). Real bodies such as blocks, crates, automobiles, and people, are obviously not particles or rigid bodies. The application of particle and rigid body mechanics to non- particulate and non-rigid bodies will result in energetic inaccuracies. Augmenting the principles of work and energy to include systems with internal structure is called Thermodynamics. 11

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 The work of friction is not computable by particulate means (F x), because its displacement is not known. The friction force arises from interactions between bits and pieces of the body and its environment that are in motion relative to the body. 12

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 13 III1 Exit Homework Problem #1

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 14 III1 Exit Homework Problem #1

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 15 III1 Exit Homework Problem #2

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 16 III1 Exit Homework Problem #2

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 17 1 of 3 Carts A and B move on frictionless tracks. Cart A has a thruster directed along the track applying a force F. Cart B has its thruster applying force F directed at 60 deg with respect to the track. Both are released and allowed to travel 2 m. During their flights, the work done on B by the thruster was 1.Zero. 2.Less than half the work done on A. 3.Half the work done on A. 4.Equal to the work done on A. F F A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 18 2 of 3 Body A is dropped from rest into vertical free fall. Body B is released from rest down a frictionless incline. The kinetic energy gained by body B is 1.Greater than that gained by A. 2.Equal to that gained by A. 3.Less than that gained by A. 4.Zero. A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 19 3 of 3 Body A is released from rest down a frictionless incline. Body B is released from rest to travel down a frictionless curvy track. It is assumed that B stays on the track and reaches the bottom. The kinetic energy gained by body B is 1.Greater than that gained by A. 2.Equal to that gained by A. 3.Less than that gained by A. 4.Zero. A B

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 How We Simplify Work Calculations Dot Product Formalism Differential Notation Path Integration Constant (Average) Force One Dimensional Motion Finite Displacement 20

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PHYS-1600/2000PHYS-1600/2000 III1 Work and EnergyNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 21 14141414 25252525 3333 PROJECTION SCREEN 6666 III1: HAND IN TODAY’S ACTIVITIES SHEETS

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Work and Energy. Scalar (Dot) Product When two vectors are multiplied together a scalar is the result:

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