System: Total Momentum v System Momentum is an extremely useful concept because momentum is conserved. It is especially useful for analyzing collisions between particles.

Find total momentum of the system: +4 m/s -1 m/s m2 = 2 kg m1 = 0.5 kg 2 kg m/s C) 4 kg m/s 3 kg m/s D) 0 kg m/s

1. Impulse = Change in Momentum 2. FDt = Change in momentum 3. If F = 0, momentum does not change. “Conservation” of momentum.

Positive change in momentum Negative change in momentum How does momentum of the system change after they collide? No external forces. +4 m/s -1 m/s Positive change in momentum Negative change in momentum Zero change in momentum

Conservation of Momentum collide! mA VA VB VA’ mB VB’ mB Just like energy, momentum cannot be created or destroyed. We can only transfer momentum from one object to another. Unlike energy, momentum does not “change forms” and momentum is a vector, not a scalar like energy, so we must use “vector math” when adding and subtracting momenta. Momentum conservation is always true - no exceptions. Internal explosions, collisions of masses in the system, do not change total momentum of the system. Total mv Before = Total mv After (if no external force on the system)

Be careful with positive and negative signs! Be careful! In energy considerations, we often use v to indicate speed (always positive), but when working with 1-D collisions v must represent velocity and can be + or -. We generally indicate rightward velocity with a positive number and leftward velocity with a negative number.

Example: Using momentum conservation +4 m/s -3 m/s ? 0 m/s m2 = 2 kg m1 = 0.5 kg Be careful! In energy considerations, we often use v to indicate speed (always positive), but when working with 1-D collisions v must represent velocity and can be + or -. We generally indicate rightward velocity with a positive number and leftward velocity with a negative number.

Momentum conserved even if many particles are involved. Total momentum before explosion = Total momentum after explosion http://www.tutorialwiz.com/explosion/images/f.jpg

Squid Propulsion (Explosion) http://www.biology.ualberta.ca/courses.hp/zool250/animations/Squid.swf Squid Propulsion (Explosion) mvtot = 0 Before After (mv)water = (mv)squid After the squid and water are moving, external forces from the surrounding water will be slowing them down, but at the instant the water is ejected from the squid, we can imagine that the water and squid have the velocities shown. This is an approximation - we approach reality by making assumptions (like no friction), then we refine our calculations later. Momentum before (0) = momentum after 0 = mWvW' + msvs' vs' = (mw/ms)vw' Total momentum = 0

Recoil: Total Momentum = 0 Before After vrecoil vbullet (mv)bullet + gun = 0 -mgunvrecoil + (mv)b = 0 Other "explosions" are treated the same way. A gun has a recoil velocity because of conservation of momentum. If the total momentum before = 0, the total momentum immediately after must be 0. If you're ever before a firing squad and they ask if you have any last requests, tell them to use a really, really big bullet and a teeny tiny gun! (Think about it and look at the equation) Why is the barrel of a rifle so long? Vfinal of bullet = acceleration x time. Want bullet to be accelerated by the interal pressure for a long time so it has a high final velocity. Momentum before (0) = momentum after 0 = mWvW' + msvs' vs' = (mw/ms)vw'

Cloud chamber photo showing tracks of particles after they’ve been blasted apart by an atom smasher. Conservation of energy, conservation of momentum and other physics principles help us determine the mass and charge of the various particles.

Elastic collision: Bounces Momentum is Conserved & No Energy "lost" Momentum is always conserved if no external forces are applied to the system! If a ball bounces back to its starting height, KE is conserved in the collision. (Demo) Superball on concrete is almost perfectly elastic. Tennis balls on court are not perfectly elastic. Atoms collide in elastic collisions - air molecules are constantly hitting each other and bounce off elastically (that’s because they “bounce” due to electric forces of repulsion). In atom smashers, atomic paricles like protons, neutrons, and electrons interact elastically.

Inelastic collision: Stick Momentum is Conserved but Energy is not Some KE has been transformed to thermal energy and sound energy. Momentum is still conserved if there are no external foces on the system.

Calculate change in momentum for each. Bouncy ball (elastic) V1 = -V V2 = V Calculate change in momentum for each. Dead ball (inelastic) V1 = -V V2 = 0

Low Friction Carts on Track Before After Inelastic v v/2 m m (at rest) v m Inelastic v = 0 v m Elastic v m

Low Friction Carts on Track Before After Elastic v1 v2 v1 v2 m m Before After Elastic m v1 v2 v2 v1

Lab: Conservation of Momentum Purpose: Experimentally (and mathematically) prove conservation of momentum in a collision or an explosion.

Lab: Conservation of Momentum Procedure: Develop and perform an experiment to prove conservation of momentum. Results should show: momentum before an event = momentum after an event. within  10%.

Things to consider: Explosion, elastic collision or inelastic collision? Will masses stay constant throughout the event? What materials will give good data? What measurement tools will you use? How to measure velocities and masses before and after the event?

Before beginning the experiment: Write down anticipated procedure and a materials list, then get materials. Do preliminary experiments to make sure your technique will work. Think through equations to make sure to measure and record correct data. Make a data table to use during experiment. Get teacher initials on prep sheet, before starting the experiment.

Momentum Conservation/Transfer Impulse on basketball and tennis ball (m+M)vbefore  mvafter Actually, the floor provides an external force and this illustrates energy conservation.