Physics 121 Tuesday March 4 2008 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 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 Rochester Physics 121 Tuesday March 4 2008 Homework set 5 is now available on the WEB and will be due 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 download the linked file Windows use right click while pointing to the movie links to download the linked file The most effective way to work on the assignment is to tackle 1 2 problems a day Note clicking on the Email instructor button sends an email to the instructor and the TAs Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Tuesday March 4 2008 Exam 1 will be returned to you during the workshops this week Any corrections to the grading of the exams can only be made by me My office hours this week have been moved from Tuesday between 11 30 am and 1 30 pm to Thursday between 11 30 am and 1 30 pm Frank L H Wolfs Department of Physics and Astronomy University of Rochester Results Midterm Exam 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Question 1 10 Exam 1 Only 8 students struggled with Q 10 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Question 11 Exam 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Question 12 Exam 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Question 13 Exam 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Results 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 thought process we can only award partial credit if we can follow what you are 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 not waiting 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 Rochester Attending class after the quiz actually makes a difference Frank L H Wolfs Department of Physics and Astronomy University of Rochester Results Midterm Exam 1 Some comments motion on circular Anytime you observe circular motion you know that the net force must be directed towards the center of the circle with a magnitude of mv2 r This force can be provided in different ways For example Tension Gravitational force Normal force Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Quiz lecture 13 The quiz today will have 4 questions Frank L H Wolfs Department of Physics and Astronomy University of Rochester The center of mass a review The position of the center of mass of a system of particles along the x axis is defined as xcm m1x1 m2 x2 1 mi xi m1 m2 M i and similar expressions for the y and z positions The motion of the center of mass is determined by the externals forces acting on the system Macm mi ai Fi Fnet ext i Frank L H Wolfs i Department of Physics and Astronomy University of Rochester Linear momentum a review The product of the mass and velocity of an object is called the linear momentum p of that object In the case of an extended object we find the total linear momentum by adding the linear momenta of all of its components Ptot pi mi vi Mvcm i i The change in the linear momentum of the system can now be calculated dPcm dvcm d Mvcm M Macm mi ai Fi Fnet ext dt dt dt i i This relations shows us that if there are no external forces the total linear momentum of the system will be constant independent of time Frank L H Wolfs Department of Physics and Astronomy University of Rochester Collisions The collision force During a collision a strong force is exerted on the colliding objects for a short period of time The collision force is usually much stronger then any external force The result of the collision force is a change in the linear momentum of the colliding objects The change in the momentum of one of the objects is equal to p f pi Frank L H Wolfs pf pi dp tf F t dt ti Department of Physics and Astronomy University of Rochester Collisions The collision impulse If we measure the change in the linear momentum of an object we will obtain information about the integral of the force acting on it p f pi pf pi dp tf F t dt ti The integral of the force is called the collision impulse J Ji Frank L H Wolfs pf pi dp tf F t dt ti Department of Physics and Astronomy University of Rochester Collisions The collision impulse Consider you are involved in a collision you first move with 55 mph and after the collision you are at rest The change in momentum is thus fixed and the collision impulse is also fixed Ji tf F t dt ti What happens to you depends on the magnitude of the force An increase in time t results in a reduction of the force Frank L H Wolfs Department of Physics and Astronomy University of Rochester Collisions The collision impulse Increasing the time required to come to a stop reduced the average force This reduction in the average force can mean the difference between life and death The human body can tolerate accelerations up to 10 15 times the gravitational acceleration An acceleration of 10g brings an object traveling at 55 mph to rest over a distance of 3 m 9 feet Frank L H Wolfs Department of Physics and Astronomy University of Rochester Collisions The collision impulse Interactions between sub atomic particles are usually studied by comparing their momenta before and after an interaction Before After The change in their momenta provides us with information about the collision impulse Determining the force from the collision impulse required a knowledge of the time dependence of the interaction Frank L H Wolfs Collision between protons Department of Physics and Astronomy University of Rochester Elastic and inelastic collisions If we consider