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 (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. Section Next Week Reminder

Announcements CAPA Set #9 due Friday at 10 pm This week in Section: Lab #3 – Momentum Reading – Chapter 7 on 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) New Conserved Quantity  Momentum

In which situation is the magnitude of the total momentum the largest? A)Situation I. B)Situation II. C)Same in both. p total = mv + 0 = mv Clicker QuestionRoom Frequency BA p total = mv-2mv=-mv Magnitudes are the same |p total |=mv

An object of mass m 1 initially moving with speed v 1i collides with another object of mass m 2 initially at rest. The objects stick together after the collision. m1m1 m2m2 v 1i v 2i =0 Totally Inelastic Collision What is the velocity of the objects after the collision? m1m1 m2m2 vfvf Before After Does that make sense?

m1m1 m2m2 v 1i v 2i =0 m1m1 m2m2 vfvf Totally Inelastic Collision Is Kinetic Energy conserved? BeforeAfter From momentum conservation Kinetic Energy Decreases (not conserved)

Elastic Collision Example An object of mass m initially moving with speed v collides with another object of mass m initially at rest. m1m1 m2m2 v v 2i =0 Before For an elastic collision, what happens afterwards? Momentum Conserved One equation, two unknowns (v 1f & v 2f ) Kinetic Energy Conserved Now we have two equations, two unknowns (v 1f & v 2f )

plug in

m1m1 m2m2 v 1i v 2i =0 Before m1m1 v 1f =0 After m2m2 V 2f Is that really correct? Demonstration….

Why is Momentum Conserved? During the collision, Newton’s Third Law applies. F 21 = - F 12 m 2 a 2 = - m 1 a 1 Assume a constant acceleration when the objects are in contact for a time  t Momentum conservation resulting from Newton 2 nd + 3 rd Law

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 asB) twice C) 3 times D) 4 times v1v1 v2v2 1 2 Clicker QuestionRoom 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 timesD) 9 times -3v v 1 2 Clicker QuestionRoom 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 thanD) unknown -3v v 1 2 Clicker QuestionRoom Frequency BA

A cannon of mass M=1000 kg fires a cannonball of mass m=10 kg with velocity v B =100m/s. What is the recoil velocity v C of the cannon? Momentum is conserved What happens to keep the cannon from going back at 1m/s?

A bullet of mass m with unknown initial horizontal velocity v 0 is fired into a large suspended block of mass M. Ballistic Pendulum Clicker QuestionRoom Frequency BA Which of the following is true for the initial collision? A)Only energy is conserved B) Only momentum is conserved C)Only kinetic Energy is conserved D) Energy and momentum are conserved E) Kinetic energy and momentum are conserved