Preparation Notes for Chapter 9 (Linear Momentum; two-three classes)


Momentum and Impulse
--------------------

Reading 9.1-9.2; Problems 9.5, 9.10


(1) Review by instructor: momentum p=mv; vector, kg m/s;
F_net = m a = m dv/dt = d(mv)/dt = dp/dt


(2) Impulse Delta p = integral (F dt) = I
I = avg F Delta t where avg F  = integral F dt /Delta t


(3) Discussion: the movie ``Speed''; in the scene at the end,
when the subway car jumps the rails to avoid crashing into the end
of the tunnel; why is this a good strategy? (many little collisions
are better than one big collision; smaller force over longer time)

(Alternatively, if class hasn't seen the movie, discuss a truck
hitting sand cans versus a bridge pillar)

(4) Problem 10


Collisions
----------

Reading 9.3-9.4; Problems 57, 61

(1) What is a collision? two particles exert large
impulsive force on each other. Assume I >>  other forces

p = p_1 + p_2; dp/dt = dp_1/dt + dp_2/dt = F_21 + F_12 = 0

p = constant; p_1i + p_2i = p_1f + p_2f 

(2) Discussion topic: can you come up with an example of a collision
where momentum is NOT conserved?

(3) Elastic collisions --> Delta K = 0; inelastic
collisions --> Delta K not equal 0; Perfectly inelastic --> objects stick 
together; discuss everyday examples of collisions; what type are they?

(4) Demo: drop a small ball above a big ball; small ball
shoots off very fast; students discuss why this happened. (Note: this is
a good demo but the mathematical discussion is long if you try to
derive it from the formulae below; if you want to derive the speed
of the lighter ball, I find it good to have an overhead with the
formula for the speed of m_1 and m_2 written down as a starting
point.)

(5) review some formulas with them (perhaps as part of
doing the problems?):

perfectly inelastic: m_1 v_1i + m_2 v_2i = (m_1+m_2)v_f

elastic: m_1 v_1i + m_2 v_2i = m_1 v_1f + m_2 v_2f

1/2 m_1 v_1i^2 + 1/2 m_2 v_2i^2 = 1/2 m_1 v_1f^2 + 1/2 m_2 v_2f^2

(6) Problem 61



Suggested Presentation Topics
-----------------------------

 Airbags, Sand Cans, and other Highway Lifesavers

 Baseball Bat Weight and Momentum Exchange with
              the Ball

 Why it *is* Important to Follow-through on that
              Swing

 Car collisions: Damage as a Function of Car Velocity

 Desirable Properties of Highway Medians


Properties of Survivable Falls



Note: these presentations can be difficult, particularly
if they are trying to measure impulse. The trick is to try to make the
collision occur over as long a time as possible. Some of these presentations
topics are less amenable to quantitative analysis, so some of the
experiments may have to be qualitative or comparisons between one setup
and another.


Content of Chapter 9
--------------------

momentum and relation to force

impulse

conservation of momentum in isolated systems

collisions: elastic, inelastic, perfectly inelastic