Download Ch 14 - Vibrations and Waves

W&O: 14.1 Notes Vibrations and Waves
Q: What constitutes a vibration, really?
A: Anything that switches to and fro; back and forth; side to side; off and on; loud and
soft; up and down, etc., is vibrating. Anything that will oscillate. A wiggle in time.
Q: What has to happen for an object to be in equilibrium?
A: Fnet = 0 therefore, the object is NOT accelerating (but can still be moving at constant
velocity).
Q: What is Hooke’s Law? Why is it “negative?”
A: Fspr = - k x ; it is a restoring force; “x” is generic
DEMO’s: Slinky off a Banister, Mass on a Spring, Pendulum
DEF: Periodic Motion = any motion that repeats
DEF: Equilibrium = Fnet = 0
DEF: Restoring Force = a force that will pull an object back to equilibrium
DEF: Simple Harmonic Motion SHM (AGAIN!) = motion resulting from an
object subject to a restoring force that is directly proportional to the
displacement of the object
DEF: Period (T) = the time needed to complete 1 full cycle; s
DEF: Amplitude (A) = the maximum displacement of an object in periodic
motion; m (cm commonly)
A Amplitude – Distance from crest to node or trough to node
DEF: Hooke’s Law = The restorative force on a spring is equal to the product
of its spring constant, k and the distance, x, the spring is either stretched or
compressed from equilibrium
F = - kx
Q: What are the units for k?
A: N/m; k measures the stiffness of the spring
Not all springs obey Hooke’s Law. Those that do are called elastic.
Q: For a graph of F versus x (displacement) for a spring, what is the physical
meaning of:
a) the area under the curve? The area would have units of Nm, so it would
be the work done by the spring = ∆ PE.
b) the slope of the line? The slope would have units of N/m, so it is the spring
constant, k.
F (N)
x (m)
PE of a Spring
When you pull or compress a spring, you change its potential energy, PE. To
do so, you must apply work, thus, the area under the curve = the work done =
the change in PE of the spring. PE of an elastic spring can be calculated using
the following formula:
PE = ½ kx2
See Ex 1, p 377
A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended
from its end.
a) Determine the spring constant
b) How much elastic PE is stored in the spring when it is stretched this far?
a) Use Hooke’s Law which relates Force exerted by a spring to the
displacement.
Divide both sides by – x and solve for k. Don’t forget SI!!!
Part a)
F = - kx
F =k
-x
b) Find the PE using PE = ½ kx2
PE = ½ (310 N/m) (0.18
= 5.0 J
m)2
- 56 N = k
-0.18 m
310 N/m = k
c)
Q: How does elastic PE relate to automobile design?
A: A car’s ability to retain its integrity following a collision depends on how
much of the KE it had before the impact to elastic PE of the frame after
impact. Many bumpers act like modified springs that store energy as the car
hits an object. After the car stops and the spring is compressed, the spring
then returns to its equilibrium position, and the car recoils from the barrier.
Pendulums
DEF: Pendulum = a bob suspended by a light string or rod that is pulled to
one side, released, and allowed to fall due to its weight. The bob then
experiences SHM, tracing out a portion of a circle, due to the combination of
FT and gravity. The net force is the vector sum of these two.
Q: Does the period of a pendulum depend on mass?
DEMO Time!!! Watch the video below!
Q: Does period depend on the length of the pendulum? Cool Youtube clip!!!
http://www.youtube.com/watch?v=yVkdfJ9PkRQ (1:45)
Period of a Pendulum
T  2
l
g
See Ex 2, p 379
A pendulum with a length of 36.9 cm has a period of 1.22 seconds. What is the
acceleration due to gravity at that location (in the world)?
l
T  2
g
So, to solve for g, you would divide both sides by 2.
Then, square both sides.
Then take the reciprocal of both sides.
Then multiply both sides by l.
Then substitute and solve. See p 379 (equation writer isn’t working!!).
Q: Why is the period of a pendulum independent of mass?
A: The restoring force depends on mg, and therefore, because anet = Fnet/m, anet
is independent of m. Because motion depends on anet and the initial conditions,
the motion is independent of the mass. Also, anet is a ratio of F due to gravity
and mass. As mass increases, so does Fg in direct proportion! The same is
true, relatively, for the decrease in mass and the decrease in Fg.
Do p 378, #’s 1 – 5; p 379, #’s 6 – 8.