This week's hands-on
experiences involve systems for which linear momentum is conserved
(CONP). CONP can be viewed as a generalization of Newton's
First Law: If no net external force acts on a system, the velocity
of the system is constant (i.e. acceleration = 0). Momentum is
a vector quantity composed of the system's mass (a scalar) multiplied by
the system's velocity (a vector, i.e. p=mv). Thus,
if no net external force acts on a system, the system's momentum
is also constant. CONP can also be viewed as a special case
of Newton's Second Law: The net external force acting on a system
equals the system's mass multiplied by it's acceleration (the familiar
F=ma). Now, sincea=dv/dt,
clearly ma=d(mv)/dt=dp/dt, the most general statement
of Newton's Second Law is that the net external force acting on a system
equals the system's rate of change of linear momentum, or F=
dp/dt. Clearly, if F=0, then dp/dt=0,
implying that p=a constant). Something that remains constant
is said to be conserved. So, we encounter the second, very
powerful conservation principle that we will consider this semester.
Last week we dealt with conservation of energy (CONE). CONP, like
CONE, is and if, then situation. If only conservative
forces act, then mechanical energy is conserved. Similarly,
if NO net external force acts, then linear momentum is conserved.
Always be very careful when attempting to apply conservation principles.
The system must meet the appropriate condition(s). In other
words, ask the if, then question for the appropriate system.
CONP applies during many collisions (or inverse collisions such as projectiles
being ejected or during explosions (many projectiles!)), providing the
system is appropriately defined. Please note that collisions
can take on a continuum between elastic (where both momentum and kinetic
energy are conserved) and perfectly inelastic (where only momentum is conserved
and the colliding bodies stick together after the collision). There
is a continuous range between those extremes where some of the system's
original kinetic energy is converted to other forms (e.g. deformed bodies
such as mangled automobile fenders). Again, momentum is a vector
quantity & must be treated as such. 1. Happy and Unhappy
Balls.
The two balls look
very similar. Let them fall together from a height of a meter or
so onto the table. Surprise! Both are made of rubber, but the
time for one ball to 'bounce back' to its original shape is ... minutes.
What types of collisions occur between the balls and the table?
2. Golf ball and ping
pong ball.
A ping pong ball
is placed on top of a golf ball, and the pair is dropped onto the floor.
What happens to the ping pong ball? Note that
during the very short collision time between the balls, the force of gravity
has no significant effect on the balls' motions.
3. Five-ball pendulum.
Note that the balls
do not touch when hanging at rest. Pull one ball aside and let it strike
the next one in line. The collision is elastic (to a very good approximation).
In a head on elastic collision between equal masses the conservation of
linear momentum and of kinetic energyallow
just one outcome. The moving ball comes to rest and the struck ball travels
off, carrying all of the initial momentum and energy. This repeats
in a series of one-on-one collisions. Next, pull two balls aside and release.
Repeat for three balls.
4. Penny-penny collision.
This is (again,
to a good approximation) an elastic collision. The coins deform slightly
during the collision but 'spring back' to their original shapes. In an
elastic collision between equal masses, one of which is initially at rest,
the angle between the directions the objects move after the collision is
ninety degrees. Check this result using two pennies. Be sure to mark
the center of the at-rest coin before thecollision
as well as the centers of the coins after the collision. Use a 3x5 card
to check the claim that the angle is a right angle.
Repeat this experiment on the air table using the pucks. Does this
idea have applications to playing pool?
5. Collisions on the
linear track.
Demonstrate totally
inelastic collisions using cars with velcro strips. Experiment with
different masses for the colliding cars.Demonstrate
elastic collisions between cars of equal masses (be sure to do the case
of one car initially at rest) and between cars ofunequal
masses.
6. Adding mass to air
puck.
While a puck is
moving on the air table drop a mass, such as a large washer, on top of
it. Be sure to just drop the mass as the puck passes underneath; do not
follow the puck with your hand before dropping the mass. What happens to
the velocity of the puck? Does the vertical impulse applied to the car
affect the momentum in the horizontal direction?
7. What makes the overhead fluorescent lights come on?
Those type lights 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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