Momentum…. just another way to talk about motion and changes in motion What Newton was really talking about in his famous paper…

Momentum The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity SI Units are kg m / s Vector quantity, the direction of the momentum is the same as the velocity’s

Momentum…or not? paper clip on desk? no Ant crawling on ground? yes

More…or…less? Godzilla on rampage or rolling tank? Shuffling zombie or speeding bullet? Moving defensive lineman or offensive guard?

How can we change the motion of these objects? Yes…you remembered…APPLY A FORCE

Impulse causes change in momentum… In order to change the momentum of an object, a force must be applied The rate of change of momentum of an object is equal to the net force acting on it Gives an alternative statement of Newton’s second law

Impulse cont. When a single, constant force acts on the object, there is an impulse delivered to the object is defined as the impulse Vector quantity, the direction is the same as the direction of the force

Impulse-Momentum Theorem The theorem states that the impulse acting on the object is equal to the change in momentum of the object If the force is not constant, use the average force applied

Case 1: impulse causes a decrease in momentum Car crash Getting hit by a punch Person doing parcour and landing on her feet

Impulse Applied to Auto Collisions The most important factor is the collision time or the time it takes the person to come to a rest This will reduce the chance of dying in a car crash Ways to increase the time Seat belts Air bags

Air Bags The air bag increases the time of the collision It will also absorb some of the energy from the body It will spread out the area of contact decreases the pressure helps prevent penetration wounds

How long does an accident take? At ~.080sec, F maximizes at 800,000 N By 0.120 sec, it’s all over!

Other situations in which longer Δ t results in less force on body Tuck and roll Bending knees when landing from a jump Roll with the punches MINIMIZE FORCE BY MAXIMIZING Δ t !!

Case 2: impulse causes an increase in momentum Bat and ball Foot and ball Starting from rest on a rollercoaster

What about maximizing Δ p ? When do you want to get something going ASAP? Roller coaster, or catapult launch on aircraft carrier: max F in short time Kicking, hitting a ball: max F but try to also maximize contact time!! Follow through!! Longer barrel on a gun maximizes time that expanding gas acts on potato, bullet, etc.

Case 3: impulse causes a change in direction…bouncing Physics you can use to win valuable prizes… Should I choose a bouncy ball or a non-bouncy ball to knock over the bottles at the Six Flags boardwalk game?

Let’s investigate change in momentum… Calculate momentum at different points in time Compare and calculate change in momentum Which experienced bigger change in momentum?

So far discussions have been about one object at a time… What if we consider all the objects that are interacting or are about to interact… Through extensive observations and data collection we would conclude that The total momentum of objects about to interact is the same as the total momentum of the objects right after they interact!!

CONSERVATION OF MOMENTUM! One of the great principles of physics! This explains the transfer of momentum in any collision, explosion, interaction of objects moving through space and time!

Σ p (before, initial) = Σ p (after, final) Add up the momenta of all objects before the interaction Add up the momenta of all objects after the interaction Before = after

Examples? Can you use the equipment available to design a demo of conservation of momentum? AIR TRACK Demos

Examples of calculations

Conservation of Momentum, cont. Mathematically: Momentum is conserved for the system of objects The system includes all the objects interacting with each other Assumes only internal forces are acting during the collision Can be generalized to any number of objects

Notes About A System Remember conservation of momentum applies to the system You must define the isolated system

Collisions! Momentum is conserved in any collision Inelastic collisions Kinetic energy is not conserved Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object Perfectly inelastic collisions occur when the objects stick together Not all of the KE is necessarily lost

More Types of Collisions Elastic collision both momentum and kinetic energy are conserved Actual collisions Most collisions fall between elastic and perfectly inelastic collisions

More About Perfectly Inelastic Collisions When two objects stick together after the collision, they have undergone a perfectly inelastic collision Conservation of momentum becomes

Some General Notes About Collisions Momentum is a vector quantity Direction is important Be sure to have the correct signs

Summary of Types of Collisions In an elastic collision, both momentum and kinetic energy are conserved In an inelastic collision, momentum is conserved but kinetic energy is not In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

Problem Solving for One -Dimensional Collisions Coordinates: Set up a coordinate axis and define the velocities with respect to this axis It is convenient to make your axis coincide with one of the initial velocities Diagram: In your sketch, draw all the velocity vectors and label the velocities and the masses

Problem Solving for One -Dimensional Collisions, 2 Conservation of Momentum: Write a general expression for the total momentum of the system before and after the collision Equate the two total momentum expressions Fill in the known values

Sketches for Collision Problems Draw “before” and “after” sketches Label each object include the direction of velocity keep track of subscripts

Sketches for Perfectly Inelastic Collisions The objects stick together Include all the velocity directions The “after” collision combines the masses