Momentum and Impulse

Physics 7B - Lecture 2Prof. John Conway

TYPO IN TEXT!!

page 8

paragraph 3

sin -> cos

cos -> sin

Welcome to Physics 7B!

I am a high energy particle physicist, studying proton-antiproton collisions at the highest energies in the world, at the Tevatron collider at Fermilab in Illinois:

Welcome to Physics 7B!

...and at CERN in Geneva, Switzerland:

CMS: Compact Muon Solenoid experiment

LHC at CERN

startup in two years!

Physics Words Physicists have very precise meanings for

these commonly used words:

momentum

energy

power

force

velocity

speed

Our job here is tolearn these concepts

and how to apply themaccurately.

Position Vectors

We use a vector with one end at the origin to indicate a position in space:

In fact the position vector may be a function of time!

y

xx^

y^

Writing Position/Velocity Vectors

In the previous example, how do we write the position vector or velocity vector?

x is changing, y is constant...we get

y

xx^

y^

h

x = vty = h

Writing Position/Velocity Vectors

how do we get the velocity vector? from calculus we know that

to do it with vectors we simply keep track separately what happens in x and y:

Writing Position/Velocity Vectors

in our case we can get the velocity vector from the position vector

y

xx^

y^

v

Momentum

The product of the mass of an object and its velocity is its momentum

y

xx^

y^

Clearly since velocity is a vector, momentum is also a vector!

m

v_

p = mv_ _

r(t)_

Weight versus Mass

one component of the momentum is the mass of an object

mass is not the same as weight! weight is the force of gravity on an object mass is how much stuff there is in the object dont say my car weighs 1000 kg say instead the mass of my car is 1000 kg how much does your 1000 kg car weigh?

Friction the interaction between two surfaces in contact

results in a force opposing relative motion of those surfaces: friction

the magnitude of the frictional force is greater for two surfaces not moving (static friction) than moving (sliding friction)

we characterize the amount of friction using a dimensionless constant called the coefficient of friction ()

example: block on table Ff = Fext< mg

Momentum and Energy

we now have two things assigned to a moving object:

momentum (p = mv) kinetic energy (K = 1/2 mv2)

are they different? cant we just use one of them and forget the other?

momentum is a vector quantity...energy is not

momentum only deals with motion - energy can change forms

_ _

1D Momentum (PRS)

Two cars are travelling in opposite directions. One has a mass of 1000 kg and the other has a mass of 1250 kg. Both have a constant speed of 10 m/s. What is the magnitude of the total momentum of the two-car system?

a. 250 kg

b. 2250 kg-m/s

c. 22500 kg-m/s

d. 2500 kg-m/s

e. 25000 kg-m/s

Conservation of Momentum

The total momentum of a closed system is always conserved (constant)

This is true even if energy is not conserved! (example: inelastic collision)

For various physical systems (cars, planets...) must consider conservation of both energy and momentum

Closed system: no external forces

Demo: carts on track

Elastic Collisions

suppose a car collides with another car, and the bumpers act as good springs

elastic collisions: energy and momentum conserved

for fun, lets say an SUV with 2000 kg mass, going 20 km/h, rear-ends a stopped Cooper Mini with mass 800 kg

what happens in such a collision? what about Mini on SUV? Mini on Mini?

Inelastic Collisions

example: two cars collide, stick together this case is actually easier to calculate: no

need to worry about conservation of energy

Inelastic Collision (PRS)

Two cars both have 1000 kg mass. One is headed east at 20 km/h, and the other is headed west at 30 km/h. They collide and stick together, but then roll without friction. Their final speed/direction is

a. 20 km/h east

b. 10 km/h east

c. 5 km/h west

d. 10 km/h west

e. 20 km/h west Use a momentum chart to do this one!

pi p pf

car 1 +20k

car 2 -30k

total -10k 0 -10k

Momentum in Two Dimensions

in general we need to keep track of the momentum of objects in all dimensions

momentum has x and y components!

Momentum in Two Dimensions

consider two cars colliding air bags deploy, no one hurt... cars crunch and stick together what happens to the momentum?

before after

Momentum in Two Dimensions

is two-car system a closed system? how do we figure out the final momentum? is there a better, more abstract example?

before after

Equilibrium

For a body to be in equilibrium, one of the conditions is that the net external force on the object is zero:

Equilibrium does not necessarily mean that the object is not moving! It just means it has constant momentum...

Impulse

For a non-closed system (subject to an external force) the change in momentum is equal to the force times the time it acts:

J = p = Ft = impulse Review: what happens to a body subject to a

force acting through a certain distance?

Demos: water rocket, ruler/pencil/chalkExample: Movie-style momentum conservation

_ _ _

Violent Movie Scene (PRS) In a (violent) movie, a man shoots a big gun at a victim, who

is thrown up off his feet, flies two or three meters through the air, and lands on his back. The shooter remains standing.

a. This is possible: the shooter knew he was going to fire, and braced himself but the victim didnt have time to prepare.

b. This is possible: the gun absorbs the momentum of the bullet going out, but the victims momentum changes when hit by the bullet.

c. This is impossible: the shooters change in momentum is opposite that of the victims, and so the shooter should be thrown of his feet too.

d. This is impossible: no gun is powerful enough to knock someone off their feet.

e. I dont watch such violent movies - whats the matter with you, anyway, Prof. Conway?

For some fun...

Ever notice that movies in general kind of exaggerate or distort physics?

See the web site:

http://www.intuitor.com/moviephysics/

Dont forget the Cartoon Laws of Physics

http://www.frostbytes.com/~jimf/humor/cartoon.laws.html

And this (serious) one has some very fun simulations:

http://www.myphysicslab.com/