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You must complete at least 5 of the 6 labs to receive a passing grade in this course.

Section Next Week Reminder. You must complete at least 5 of the 6 labs to receive a passing grade in this course. If you missed a lab, you can make it up during one of two Review/Lab make-up weeks: October 24-28 (labs 1-3) December 5-9 (labs 4-6)

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You must complete at least 5 of the 6 labs to receive a passing grade in this course.

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  1. Section Next Week Reminder • You must complete at least 5 of the 6 labs to receive a passing grade in this course. • If you missed a lab, you can make it up during one of two Review/Lab make-up weeks: • October 24-28 (labs 1-3) • December 5-9 (labs 4-6) • Even if you don’t need to make up a lab, you still must attend your section those weeks for the Review Recitation. • To make up a lab, contact your TA ahead of time. You will need to arrange attending twice: (1) for lab make-up and (2) for the review recitation. You can attend any other section (in addition to your regular section), if you have that section’s TA permission in advance.

  2. Announcements • CAPA Set #9 due Friday at 10 pm • This week in Section: Lab #3 – Momentum • Reading – Chapter 7 on Momentum

  3. New Conserved Quantity Momentum Kind of like kinetic energy (associated with motion). However, not in units of Joules (instead kg m/s) and so not an energy. In addition to total energy being conserved in every collision, the total momentum vector is also conserved! Conservation of Momentum (in one-dimension)

  4. Clicker Question Room Frequency BA In which situation is the magnitude of the total momentum the largest? Situation I. Situation II. Same in both. Magnitudes are the same |ptotal|=mv ptotal = mv+ 0 = mv ptotal = mv-2mv=-mv

  5. Totally Inelastic Collision An object of mass m1 initially moving with speed v1i collides with another object of mass m2 initially at rest. The objects stick together after the collision. v1i v2i=0 Before m1 m2 After vf m1 m2 What is the velocity of the objects after the collision? Does that make sense?

  6. Totally Inelastic Collision Is Kinetic Energy conserved? Before After v1i v2i=0 vf m1 m1 m2 m2 From momentum conservation Kinetic Energy Decreases (not conserved)

  7. Elastic Collision Example An object of mass minitially moving with speed vcollides with another object of mass minitially at rest. v v2i=0 Before m1 m2 For an elastic collision, what happens afterwards? Momentum Conserved Kinetic Energy Conserved One equation, two unknowns (v1f & v2f) Now we have two equations, two unknowns (v1f & v2f)

  8. plug in

  9. v1i Before v2i=0 m1 m2 V2f After v1f=0 m2 m1 Is that really correct? Demonstration….

  10. Why is Momentum Conserved? During the collision, Newton’s Third Law applies. F21 = - F12 m2 a2= - m1a1 Assume a constant acceleration when the objects are in contact for a time Dt Momentum conservation resulting from Newton 2nd + 3rd Law

  11. Clicker Question Room Frequency BA Two masses of size m and 3m are at rest on a frictionless table. A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart. After the masses separate, the speed of m is _______ the speed of 3m. A) the same as B) twice C) 3 times D) 4 times v2 v1 2 1

  12. Clicker Question Room Frequency BA Two masses of size m and 3m are at rest on a frictionless table. A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart. After the masses separate, the KE of m is _______ the KE of 3m. A) the same as B) twice C) 3 times D) 9 times v -3v 2 1

  13. Clicker Question Room Frequency BA Two masses of size m and 3m are at rest on a frictionless table. A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart. While the spring is in contact with the masses, how does the magnitude of the force of m on 3m compare to the magnitude of the force of 3m on m? A) the same as B) less than C) greater than D) unknown v -3v 2 1

  14. A cannon of mass M=1000 kgfires a cannonball of mass m=10 kgwith velocity vB=100m/s. What is the recoil velocity vCof the cannon? Momentum is conserved What happens to keep the cannon from going back at 1m/s?

  15. Clicker Question Room Frequency BA Ballistic Pendulum A bullet of mass m with unknown initial horizontal velocity v0is fired into a large suspended block of mass M. Which of the following is true for the initial collision? Only energy is conserved B) Only momentum is conserved Only kinetic Energy is conserved D) Energy and momentum are conserved E) Kinetic energy and momentum are conserved

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