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by Liz "Porkchop" Pociask (pronounced PO-chask), Yassy "Q-tip" Qutub, Brennan
"Stud" Denny, and Naz "Kami" Kazi. Special thanks to Mr Tipps, Mr
Porter, and our agent Sandy. uhhh...that's about it
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First let's talk about SHM--Simple Harmonic Motion. This can be used to understand how springs and pendulums work.
One important thing about springs is Hooke's Law.
Hooke's Law is used to find the force on a spring.
F is the force on the spring.
k is the spring constant (which
varies for every spring..we'll talk more about that in a minute.)
x is the distance from equilibrium
of the mass.
Since most of this sounds like gibberish
(maybe), let's explain.
A spring with a mass hung on it
is at equilibrium when the mass is where it is "happy." The mass stays
at a location where all the forces balance out. Now say some jerk pulls
on the mass. The distance he pulls it from where it was before is x. The
mass will bounce up and down on the spring in simple harmonic motion. (Be
careful, Williams does a demo with this in class...a bouncy spring swing
thing.)
SAMPLE PROBLEM USING HOOKE'S LAW
A spring is in equilibrium and
hung vertically. A mass of 2 kg. is suspended on the spring. The mass is
then pulled down 10 cm. and let go. Calculate the spring constant for this
particular spring.
How it's done:
Using Hooke's Law, F=-kx, isolate
the k. That's the easy part. F/x=k.
The force acting on the mass is
the force of gravity, mg.
m=2 kg g=10 m/s2
Therefore F=mg=20 N.
Then, you put in x. Be careful,
it's in centimeters. Convert it to meters, .1 m.
F/x=20 N/.1m=200 N/m
The spring constant, k, is 200 N/m.
*Note: the negative sign in Hooke's Law means that the force is a restoring force acting against the others. It really does not make the end answer negative. Also, the diagram above uses "y" in place of "x" which is just another example of how variables vary for different books or people...maybe that's why they are VARYables!
click here for more info!
http://www.physics.gatech.edu/academics/tutorial/phys2121/Chapter%2016/SHM.html
When an object oscillates on a spring, neither its acceleration nor velocity is constant. Williams will ask you time and again where during its motion is the acceleration zero or at its maximum, and same thing with the velocity.
Some key definitions in understanding
this unit:
Amplitude: the maximum
dispacement from equilibrium; A
Period: the time it takes
to undergo one complete cycle of motion; T
Angular frequency: frequency
in radians/second; symbol is the lowercase omega, w
As seen in the diagram below,
the velocity is at a maximum when the mass passes through the point of
equilibrium.
Maximum velocity can be found
using the following equation:
The acceleration is at a maximum
when it passes through the point of amplitude (farthest displacement).
Its velocity at this point, however, is zero.
The period of motion (defined
above) can be found using the following equation:
in which T is the time of period,
m is the mass of the oscillating object, and k is the spring constant.
The frequency is simply the
reciprocal of the period, since the frequency is oscillations per time,
whereas the period is time per oscillation.
In order to calculate w, the
angular frequency, you must first know the regular frequency or the spring
constant/mass. To find w, use the following formulas.
A pendulum is another major concept in SHM. A pendulum
is a mass attached to the end of a length of string or wire that undergoes
a semicircular motion (think grandfather clock). Hooke's law applies to
a pendulum, too, only the "k" constant is found using this equation:
M is the mass on the string and g is gravity. l is the length of the pendulum.
The period of a pendulum can be found using an equation
similar to the period for an oscillating mass on a spring.
Note: the angle and the mass don't affect the period of motion, as is evident in the above equation.
Energy is conserved in pendulums and simple harmonic motion, too.At the top of the swing, where the velocity is zero, all the energy is GPE (gravitational potential energy). At the bottom of the swing, all the energy is KE (kinetic energy). Therefore, if you would like to calculate the velocity at the bottom of the swing, set up the equation so that you know the height difference from the highest point to the lowest point. (Hint: you may want to use triangle trig.) We're not going to discuss energy relationships too much CUZ IT'S NOT OUR UNIT DORKUS! But just remember how to find max. velocity.
If you want to calculate the distance of displacement
of the mass on a pendulum, use angle measurements. If the angle is less
than 15 degrees, then use the straight line distance. But if the angle
that it swings over is more than 15 degrees, you must use the diplacement
using what you know about circle arcs and geometry using the given angle.
Centripetal motion is when an objet is traveling in a
circle.
An object in centripetal motion experiences a constant
acceleration towards the center. The velocity is constant in magnitude
but changing in direction. The acceleration is constant. The centripetal
force is not a force that can be drawn on a free-body diagram because it
is a net force. To calculate the centripetal force, use this equation:
where F is the force, = is the equal sign, m is the mass, v is the velocity, 2 is the exponent, dork, / is the division sign, r is the radius of the circle
Fnet=ma, so to find the acceleration use the following
equation:
click
here to see a kick-butt site
Let's start by telling you about
the different parts of the wave. Here are some key terms you may need to
know to understand waves.
Node: a point on a wave that
doesn't move (like the party-pooper who refuses to do the "wave" at a pep
rally)
Antinode: the point farthest
from the median line of a wave
Amplitude: the "top of the bulge"
on a wave; maximum displacement
Trough: the low/bottom of the
wave; a "negative" amplitude
Crest: a toothpaste, recommended
by 9 out of 10 dentists; the highest part of a wave
Longitudinal wave: compression
wave, like sound
Transverse wave: like the slinky
wave, it travels on a line
Mechanical wave: uses a medium
anddisturbance; sound is mechanical and uses air as its medium
Non-mechanical wave: uses no
known medium; light is an example
Wavelength: the distance from
one crest to the next crest, or one point on a wave to the next same location;
symbol is
lambda (looks
like an upside-down Y)
The lower wave shown above is a compression wave. The
dense spots are the compression, and the sparse spots are rarefactions.
A compression wave can also be made on a slinky by quickly pushing one
end in and watching the dense spot travel along the slinky.