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ROCHESTER PHY 121 - Lecture 13 Notes

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1Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, March 4, 2008.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, March 4, 2008.• Course Information• Quiz• Topics to be discussed today:• Conservation of linear momentum (a brief review)• One- and two-dimensional collisions (elastic and inelastic)Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, March 4, 2008.• Homework set # 5 is now available on the WEB and will bedue next week on Saturday morning, March 8, at 8.30 am.• To download the collision videos:• OSX: use control-click while pointing to the movie links to downloadthe linked file.• Windows: use right-click while pointing to the movie links todownload the linked file.• The most effective way to work on the assignment is totackle 1 - 2 problems a day.• Note: clicking on the “Email instructor” button sends anemail to the instructor and the TAs.2Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, March 4, 2008.• Exam # 1 will be returned to you during the workshops thisweek.• Any corrections to the grading of the exams can only bemade by me.• My office hours this week have been moved from Tuesdaybetween 11.30 am and 1.30 pm to Thursday between 11.30am and 1.30 pm.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterResults Midterm Exam # 1.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterQuestion 1 - 10, Exam # 1.Only 8 students struggled with Q 10.3Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterQuestion 11, Exam # 1.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterQuestion 12, Exam # 1.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterQuestion 13, Exam # 1.4Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterResults Midterm Exam # 1.• Observations:• Circular motion causes many problems.• Some students had difficulty getting started - what approach to take.• Many students had difficulty with clearly expressing their thoughtprocess (we can only award partial credit, if we can follow what youare doing).• Recommendations:• If your score is below 50% you really need to ask why?• Are you giving this course enough time?• Do you come to lecture (and stay after the quiz)?• Do you go to workshops?• Do you work on the homework assignments in an efficient manner (notwaiting until the last moment to start working on it)?• Do you look at the homework solutions?• Did you look at the practice exam?• Did you feel prepared? If not, why not? If not, did you ask for help?Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterAttending class (after the quiz) actually makesa difference.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterResults Midterm Exam # 1• Some comments on circularmotion:• Anytime you observe circularmotion, you know that the netforce must be directed towards thecenter of the circle with amagnitude of mv2/r.• This force can be provided indifferent ways. For example:• Tension• Gravitational force• Normal force5Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Quiz lecture 13.• The quiz today will have 4 questions!Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe center of mass (a review).• The position of the center of mass of a system of particlesalong the x-axis is defined asand similar expressions for the y and z positions.• The motion of the center of mass is determined by theexternals forces acting on the system: xcm=m1x1+ m2x2m1+ m2=1Mmixii! M!acm= mi!aii!=!Fii!=!Fnet ,extFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterLinear momentum (a review).• The product of the mass and velocity of an object is calledthe linear momentum p of that object.• In the case of an extended object, we find the total linearmomentum by adding the linear momenta of all of itscomponents:• The change in the linear momentum of the system can nowbe calculated:• This relations shows us that if there are no external forces,the total linear momentum of the system will be constant(independent of time). !Ptot=!pii!= mi!vii!= M!vcm d!Pcmdt=ddtM!vcm( )= Md!vcmdt= M!acm= mi!aii!=!Fii!=!Fnet ,ext6Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCollisions.The collision force.• During a collision, a strong forceis exerted on the colliding objectsfor a short period of time.• The collision force is usuallymuch stronger then any externalforce.• The result of the collision force isa change in the linear momentumof the colliding objects.• The change in the momentum ofone of the objects is equal to !pf!!pi= d!p!pi!pf"=!F t( )dttitf"Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCollisions.The collision impulse.• If we measure the change in thelinear momentum of an object wewill obtain information about theintegral of the force acting on it:• The integral of the force is calledthe collision impulse J: !pf!!pi= d!p!pi!pf"=!F t( )dttitf" !Ji= d!p!pi!pf!=!F t( )dttitf!Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCollisions.The collision impulse.• Consider you are involved in acollision: you first move with 55mph and after the collision youare at rest.• The change in momentum is thusfixed and the collision impulse isalso fixed:• What happens to you depends onthe magnitude of the force! Anincrease in time Δ t results in areduction of the force. !Ji=!F t( )dttitf!7Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCollisions.The collision impulse.• Increasing the time required tocome to a stop reduced theaverage force.• This reduction in the averageforce can mean the differencebetween life and death.• The human body can tolerateaccelerations up to 10 - 15 timesthe gravitational acceleration.• An acceleration of 10g brings anobject traveling at 55 mph to


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ROCHESTER PHY 121 - Lecture 13 Notes

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