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UT Arlington PHYS 1443 - Lecture Notes

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Slide 1AnnouncementsReminder: Special Project for Extra CreditSpecial ProjectLet’s think about the meaning of work!Work Done by the Constant ForceScalar Product of Two VectorsExample of Work by Scalar ProductExample of Work w/ Constant ForceEx. 7.1 Work done on a crateEx. Bench Pressing and The Concept of Negative WorkEx. Accelerating a CrateEx. Continued…Work Done by the Varying ForceKinetic Energy and Work-Kinetic Energy TheoremWork and Kinetic EnergyWork-Kinetic Energy TheoremExample for Work-KE TheoremEx. Deep Space 1Ex. Satellite Motion and Work By the GravityWork and Energy Involving Kinetic FrictionExample of Work Under FrictionEx. Downhill SkiingEx. Now with the X componentMonday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu1PHYS 1443 – Section 001Lecture #9Monday, June 20, 2011Dr. Jaehoon Yu•Work Done By A Constant Force•Scalar Product of Vectors•Work Done By A Varying Force•Kinetic Energy, Work-Kinetic Energy Theorem•Work and Energy Involving Kinetic Friction•Potential Energy and the Conservative ForceToday’s homework is homework #5, due 10pm, Thursday, June 23!!Monday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu2Announcements•Mid-term exam–8 – 10am, in the class tomorrow, Tuesday, June 21, 2011–Covers: CH 1.1 – what we finish today (CH7.4) plus Appendices A and B–Mixture of free response problems and multiple choice problems•Bring the special project #3 during the intermissionMonday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu3Reminder: Special Project for Extra CreditA 92kg astronaut tied to an 11000kg space craft with a 100m bungee cord pushes the space craft with a force P=36N in space. Assuming there is no loss of energy at the end of the cord, and the cord does not stretch beyond its original length, the astronaut and the space craft get pulled back to each other by the cord toward a head-on collision. Answer the following questions.•What are the speeds of the astronaut and the space craft just before they collide? (10 points)•What are the magnitudes of the accelerations of the astronaut and the space craft if they come to a full stop in 0.5m from the point of initial contact? (10 points)•What are the magnitudes of the forces exerting on the astronaut and the space craft when they come to a full stop? 6 points)•Due is Wednesday, June 22.Monday, June 20, 2011 4Special Project•Derive the formula for the gravitational acceleration ( ) at the radius from the center, inside of the Earth. (10 points)•Compute the fractional magnitude of the gravitational acceleration 1km and 500km inside the surface of the Earth with respect to that on the surface. (6 points, 3 points each)•Due at the beginning of the class Monday, June 27( )in ER R<ingPHYS 1443-001, Spring 2011 Dr. Jaehoon YuLet’s think about the meaning of work!•A person is holding a grocery bag and walking at a constant velocity.•Is he doing any work ON the bag? –No–Why not?–Because the force he exerts on the bag, Fp, is perpendicular to the displacement!!–This means that he is not adding any energy to the bag.•So what does this mean?–In order for a force to perform any meaningful work, the energy of the object the force exerts on must change!! •What happened to the person?–He spends his energy just to keep the bag up but did not perform any work on the bag.Monday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu5Monday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu6xyWork Done by the Constant ForceA meaningful work in physics is done only when the net forces exerted on an object changes the energy of the object.MFθFree Body DiagramMdgF M g=ur urNFurθFurWhich force did the work?W =Force FurHow much work did it do?What does this mean?Physically meaningful work is done only by the component of the force along the direction of the motion of the object.Unit?N m�Work is an energy transfer!! Fur∑( )⋅dur=cosFd q (for Joule)J=Why? What kind? ScalarMonday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu7Scalar Product of Two Vectors •Product of magnitude of the two vectors and the cosine of the angle between them Aur⋅Bur≡•Operation is commutative Aur⋅Bur= AurBurcosθ =•Operation follows the distribution law of multiplication Aur⋅Bur•How does scalar product look in terms of components? Aur=Axi∧+Ayj∧+Azk∧ Bur=Bxi∧+Byj∧+Bzk∧ Aur⋅Bur= Axi∧+Ayj∧+Azk∧⎛⎝⎜⎞⎠⎟⋅ Bxi∧+Byj∧+Bzk∧⎛⎝⎜⎞⎠⎟x x y y z zA B i i A B j j A B k k� � � � � �� �= �+ �+ �� �� �kkjjii ikkjji•Scalar products of Unit Vectors Aur⋅Bur= AurBurcosθ BurAurcosθ = Bur⋅ Aur Aur⋅ Bur+Cur( )=10x xA B +y yA B +z zA B=0 cross terms+ +Aur⋅CurMonday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu8Example of Work by Scalar ProductA particle moving on the xy plane undergoes a displacement d=(2.0i+3.0j)m as a constant force F=(5.0i+2.0j) N acts on the particle. a) Calculate the magnitude of the displacement and that of the force. dur= Fur=b) Calculate the work done by the force F.Wjiji 0.20.50.30.2)(166100.20.30.50.2 Jjjii YXdFCan you do this using the magnitudes and the angle between d and F?W =22yxdd   m6.30.30.22222yxFF   N4.50.20.522 Fur⋅dur= Fur⋅dur= FurdurcosθMonday, June 20, 2011 9Example of Work w/ Constant ForceA man cleaning a floor pulls a vacuum cleaner with a force of magnitude F=50.0N at an angle of 30.0o with East. Calculate the work done by the force on the vacuum cleaner as the vacuum cleaner is displaced by 3.00m to East.Does work depend on mass of the object being worked on?MF30oMdW W =50.0×3.00×cos30o=130JNoWhy ?This is because the work done by the force bringing the object to a displacement d is constant independent of the mass of the object being worked on. The only difference would be the acceleration and the final speed of each of the objects after the completion of the work!! Fur∑( )⋅dur= Fur∑( )durcosθPHYS 1443-001, Spring 2011 Dr. Jaehoon YuMonday, June 20, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu10Ex. 7.1 Work done on a crateA person pulls a 50kg crate 40m along a horizontal floor by a constant force Fp=100N, which acts at


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UT Arlington PHYS 1443 - Lecture Notes

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