This week's hands-on
experiences include a further look at collisions, CONP & an introduction
to rotational motion (kinematics and dynamics). Last
week we focussed upon CONP, the if, then conditions that must be
satisfied for momentum to be conserved and "types of collisions" during
which momentum was conserved, i.e. the continuum between elastic and perfectly
inelastic collisions. This week, we look again at such collisions
and systems in which linear momentum is conserved, and we begin considering
rotational motion. The latter serves as a prelude to the third (and
last) conservation principle that we well investigate this semester:
Conservation of Angular Momentum (CONL) - but that's the primary topic
for next week. 1. Collisions
& CONP.
The linear track, it's baaaaaack.
Please investigate the variety of elastic and perfectly inelastic two-body
collisions available via the linear track cars. This time around,
we'll try to use the sonar ranger rig introduced earlier in the context
of 1-D motion. Try to correlate the various collisions you arrange
with the corresponding plots of x vs t, v vs t and a vs t.
2. Perfectly inelastic
raw egg - bed sheet collisions.
You may have gotten the idea last week that perfectly
inelastic collisions were among the most violent collisions of all.
To disabuse you of that notion we offer you the example of the raw egg
colliding with a bed sheet. PLEASE PERFORM THIS EXPERIMENT OUTSIDE
- just in case you miss the bed sheet when you throw the egg. This
situation is not significantly different from that experienced by automobile
drivers and passengers that collide with air bags shortly after the automobile
in which they are riding collides (rather violently) with another object.
Perfectly inelastic clearly does not necessarily equal maximum violence.
In terms of impulse (which equals the change in momentum), for a
given change in linear momentum, the longer the time required for the change,
the smaller the force required to effect the change. F still equals
ma. The old saying that "it's not the long fall, but the sudden stop
that hurts," is turned around here. Think about it! It's an
important consideration.
3. The Great
Race.
Ever wonder why your instructor has, until now, insisted
on talking about objects sliding down inclines rather than rolling
down inclines? This little personal experience will show you why!
If the object also rotates, the effects of that rotation must be accounted
for. How does the concept of rotational inertia come into play in
the this situation? How many different linear kinematics and dynamics
principles can be generalized to the case where rotation is present.
Try out linear vs rotational kinematics analogies. How about
linear vs rotational dynamics analogies, e.g. the rotational analog
of the Work-Energy Principle (WEP), the inclusion of rotational kinetic
energy in the Principle of Conservation of Mechanical Energy (CONE).
What makes the the objects roll in the first place? What are the
rotational analogs of displacement, velocity, acceleration, force and momentum?
Translation and rotation, how are they similar, what are the differences?
You have become intimately familiar with linear kinematics and dynamics.
Are rotational kinematics and dynamics fundamentally different -
NO! They are completely analogous. Learning by analogy is a
very powerful way to extent existing knowledge into new (analogous) areas.
Use it - WHEN AN ANALOGY IS APPROPRIATE!!
4. What causes rotation?
We translate all
the time (i.e. we move in straight line segments). We don't rotate
very much (if you think about it, that's what makes many of the rides at
amusement parks "amusing" - they cause us to rotate). We offer
you a bicycle wheel and some weights. Place them at various points
around the wheel and along a radius (a spoke), and observe the resulting
rotational motion. Force = mass (inertia) x acceleration, yea,
but torque = rotational inertia x angular acceleration. Analogous?
Yes! But how is torque related to force?
5. Torque Wrench?
What is torque, and what does it mean to me? Torque = r X
F. The CROSS
PRODUCT!
Ever change a flat
tire? You have to cause the lug nuts to rotate. How do you
do that most effectively. Recall the song...."I don't want to work......"
What is the rotational analog of work? If you want to avoid it, you
have to understand it - from all points of view! Work = force
dot displacement. What is the angular analog of force?
What is angular analog of displacement? Exert some torques, while
doing the minimum amount of work. How do you arrange to do the minimum
amount of work while exerting the maximum amount of torque? Does
the cross product make some sense to you?
6. Back to collisions
& CONP. What makes the (fluorescent) lights come on?
Hey, let's go on
a field trip to one of the basement labs. Collisions & CONP in
gas discharges. Gas discharge light sources pass a current
through a gas. Electrons collide with the gas atoms. The collisions
can be either elastic or inelastic.
What is the result of an elastic collision between a gas atom and an electron?
What would be the result of an inelastic collision between
a gas atom and an electron. Keep in mind that atoms have only certain,
well-defined, allowed internal energy levels.
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