9.2 Conservation of Momentum A collision is an interaction between two objects which have made contact with each other In a collision, there is a force on both objects which causes an acceleration of both objects.

9.2 Conservation of Momentum The rightward moving seven-ball experiences a leftward force which causes it to slow down; the eight-ball experiences a rightward force which causes it to speed up

under certain circumstances momentum is a conserved quantity 9.2 Conservation of Momentum under certain circumstances momentum is a conserved quantity – a quantity that remains unchanged as a system evolves. System – a set of objects that interact with each other Closed system – a system that does not gain or lose mass Two types of forces can act on a system of objects Internal – forces the objects in the system exert on each other External – forces exerted on the objects from a source external to the system

9.2 Conservation of Momentum isolated system - the net external force acting on the system is zero (no system on Earth can be completely isolated) The momentum of each ball may change as a result of the collision (each departing with a velocity different than what it started with) The sum of their momenta is found to be the same before as after the collision Sum of momenta before: mAvAi + mBvBi Sum of momenta after: mAvAf + mBvBf =

momentum before = momentum after 9.2 Conservation of Momentum Law of Conservation of Momentum: The total linear momentum of a closed, isolated system remains constant (is conserved). m1v1i + m2v2i = m1v1f + m2v2f momentum before = momentum after

There is no net external force during the collision. 9.2 Conservation of Momentum Frictionless Pool Table (Two-ball system) There is no net external force during the collision. The total momentum of this two-ball system IS conserved.

Frictionless Pool Table (Two-ball system) 9.2 Conservation of Momentum Frictionless Pool Table (Two-ball system) The instant before the balls collide, a hole opens in the table beneath them. During the collision, an external force causes the balls to accelerate downward causing a change in the total momentum. Total momentum of this two-ball system is NOT conserved.

The force applied by ball 2 causes a net external force. 9.2 Conservation of Momentum Frictionless Pool Table (One-ball system) The force applied by ball 2 causes a net external force. The total momentum of the system is NOT conserved.

9.2 Conservation of Momentum Starting from rest, two skaters push off against each other on smooth level ice, where friction is negligible. As figure (a) shows, one is a woman (mw = 54 kg), and one is a man (mm = 88 kg). Part (b) of the drawing shows that the woman moves away with a velocity of vf1 = +2.5 m/s. Find the recoil velocity vf2 of the man.

A rocket, containing fuel at rest in some reference frame. 9.2 Conservation of Momentum A rocket, containing fuel at rest in some reference frame. In the same reference frame, the rocket fires and gases are expelled at high speed out the rear. The total vector momentum remains zero.

9.2 Conservation of Momentum A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun is pushed backward and the bullet is pushed forward. The acceleration of the recoiling gun is ... a) greater than the acceleration of the bullet b) smaller than the acceleration of the bullet c) the same size as the acceleration of the bullet

9.2 Conservation of Momentum Calculate the recoil velocity of a 5.0 kg rifle that shoots a 0.050 kg bullet at a speed of 120 m/s.

9.2 Conservation of Momentum Movies often show someone firing a gun loaded with blanks. In a blank cartridge the lead bullet is removed, and the end of the shell casing is crimped shut to prevent the gunpowder from spilling out. When a gun fires a blank, is the recoil greater than, the same as, or less than when the gun fires a standard bullet?

Momentum is conserved in two-dimensional collisions as well 9.2 Conservation of Momentum Momentum is conserved in two-dimensional collisions as well x-component momentum conserved y-component momentum conserved

9.2 Conservation of Momentum A 1325 kg car, C, moving north at 27.0 m/s, collides with a 2165 kg car, D, moving east at 11.0 m/s. The two cars are stuck together. In what direction and with what speed do they move after the collision?

9.2 Conservation of Momentum A 65.0 kg ice skater moving forward with a velocity of 2.50 m/s throws a 0.150 kg snowball forward with a velocity of 32.0 m/s. What is the velocity of the skater after throwing the snowball. Disregard friction. A second skater initially at rest with a mass of 60.0 kg catches the snowball. What is the velocity of the second skater?

9.2 Chapter 9 Vocabulary impulse momentum impulse-momentum theorem closed system isolated system internal forces external forces law of conservation of momentum