PHYSICS 103 Lecture 14 Agenda for Today Momentum

PHYSICS 103: Lecture 14 Agenda for Today: • Momentum and Energy Conservation Newton’s cradle demo

Momentum • Momentum is the product of mass times velocity of an object P = m v • Momentum is a vector quantity (same direction as v) Units = kg m/s

NEWTON’S LAWS OF MOTION Second LAW: AW The force on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force. F=m. a a = Dv/Dt F = m. Dv/Dt F. Dt = m. Dv Impulse =F. Dt Dp = m. Dv Change in “momentum”

NEWTON’S LAWS OF MOTION Third LAW: AW For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object. (For every action there is an equal but opposite reaction) F. Dt = m. Dv If the external force acting on a system of objects is zero, the total momentum is conserved.

CONSERVATION OF MOMENTUM During a collision, there are no external forces, so momentum is conserved. This means: total momentum before collision = total momentum after collision

Types of Collisions • Elastic - no kinetic energy is lost during collisions (things bounce off each other) • Partially Inelastic - some kinetic energy is lost during collisions • Perfectly Inelastic - objects stick together

Class Demo: Example of Elastic Collisions Behavior: Number of balls in always equals the number of balls out. What accounts for the behavior of this system of swinging balls?

How high up will the struck ball go? h

Behavior of balls is consistent with conservation of momentum Total momentum before collision: mv = 0+0+mv Total momentum after collision: mv = mv+0+0

Other possibilities also conserve momentum 2 balls in, one ball out Momemtum before collision: 2 mv = 0+0+0+(2 m)v Momentum after collision: 2 mv = m(2 v)+0+0 momentum is conserved

Other possibilities also conserve momentum 2 balls in, 4 balls out Momentum before collision: 2 mv = 0+0+0+(2 m)v Momentum after collision 2 mv = (4 m)(0. 5 v)+0 momentum is conserved What Physics are we missing?

Energy Conservation Elastic collision KE is conserved

Case: two balls in, one ball out with twic the speed Energy is not conserved! There is only one case where BOTH energy and momentum are conserved

Main Points from Today’s Lecture • Momentum You should understand impulse, momentum, conservation of momentum in different kinds of collisions. You should review the example problems in this lecture.

Read Ch. 7 HW CH 7: Q 2, Q 6, Q 8, Q 9, Q 17, E 2, E 9, E 10, CP 5 (for next week)