PHYS 1443 Section 001 Lecture 9 Monday June 20 2011 Dr 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 Force Today s homework is homework 5 due 10pm Thursday June 23 Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 1 Announcements 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 intermission Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 2 Reminder Special Project for Extra Credit A 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 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 3 Special 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 Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 4 Let 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 Yu 5 Work Done by the Constant Force A meaningful work in physics is done only when the net forces exerted on an object changes the energy of the object F M y Free Body Diagram M x d Which force did the work How much work did it do Force Why F d What kind Scalar Unit Physically meaningful work is done only by the component What does this mean of the force along the direction of the motion of the object Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Work Jaehoon Yu is an energy transfer 6 Scalar Product of Two Vectors Product of magnitude of the two vectors and the cosine of the angle between them A B A B cos A B A B cos B A cos Operation is commutative B A Operation follows the distribution A B C A B A C law of multiplication Scalar products of Unit Vectors How does scalar product look in terms of components A Ax i Ay j Az k B Bx i By j Bz k A B Ax i Ay j Az k Bx i By j Bz k A B Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 0 7 Example of Work by Scalar Product A 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 Y d F X a Calculate the magnitude of the displacement and that of the force d F b Calculate the work done by the force F F d Can you do this using the magnitudes and the angle between d and F F d F d cos Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 8 Example of Work w Constant Force A 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 F M 30o d M F d F d cos W 50 0 3 00 cos 30 130J Does work depend on mass of the object being worked on Why No 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 Monday June 20 2011 PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 9 Ex 7 1 Work done on a crate A person pulls a 50kg crate 40m along a horizontal floor by a constant force Fp 100N which acts at a 37o angle as shown in the figure The floor is rough and exerts a friction force Ffr 50N Determine a the work done by each force and b the net work done on the crate What are the forces exerting on the crate Fp Ffr FG mg FN mg Which forces perform the work on the crate Fp Work done on the crate by FG Work done on the crate byFN Work done on the crate by Fp Work done on the crate by Ffr Ffr WG FG x mg cos 90 x 0J WN FN x mg cos90 x 100 cos90 40 0J W p F p x F p cos37 x 100 cos37 40 3200J W fr F fr x F fr cos180 x 50 cos180 40 2000J So the net work on the crate Wnet WN WG W p W fr 0 0 3200 2000 1200 J This isMonday the same as June 20 2011 Wnet F x FN x FG x Fp x F fr x PHYS 1443 001 Spring 2011 Dr Jaehoon Yu 10 Ex Bench Pressing and The Concept of Negative Work A weight lifter is bench pressing a barbell whose weight is 710N a distance of 0 65m above his chest Then he lowers it the same distance The weight is raised and lowered at a constant velocity …
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