Transcript Do Now 8/28/12 - North Hills Preparatory

Do Now
5 min –
Explain why a pendulum oscillates using words and
pictures. Work INDIVIDUALLY.
5 min –
Share with your table partner … add/make changes to your
answer if necessary.
Vocab Review!
What does the word oscillation mean?
back and forth movement
When is oscillatory motion is called
periodic motion?
 If the motion repeats
 If the motion follows the same path
in the same amount of time
We refer to these repeating units of periodic motion
motion as… cycles
The time it takes to complete one cycle is called the …
period (T)
Example:
Earth’s rotation has a period of 24 hours, or 86,400 s.
Simple Harmonic Motion
Pendulums and springs are special examples of motion
that not only oscillatory and periodic, but also simple
harmonic.
Simple harmonic motion is a type of periodic motion in
which the force that brings the object back to equilibrium
is proportional to the displacement of the object.
e.g. greater displacement = greater force
Restoring Force - CFUs
In which position(s) is the restoring force
Of the pendulum …
… greatest? A, G
… zero?
D
… angled downward and towards
the right? G, F, E
A
B
C
D
E
In which position(s) is the
restoring force of the spring …
… greatest? G
… zero? A
… directed upwards? B, C, D, E, F, G
Springs can also be compressed!
Any elastic (stretchable) material will act somewhat like a
spring.
F
G
Calculating restoring (net) force
In pendulums …
In springs …
Look at the diagram.
Fspring = kx
where
k is spring constant,
x = displacement
What forces cancel out?
T and mgcosθ cancel out … we know
because there is no a in that direction
What is the net force?
mgsinθ
We do: Calculating restoring (net) force
An engineer measured the force
required to compress a spring.
Force (N) Displacement
(mm)
2
1.0
1) Based on the data, what is the
spring constant?
3
1.5
4
2.0
2) Predict the force required to
compress the spring by 3.5 mm.
5
2.5
6
3.0
1) k = 2 N/mm = 0.002 N/m
2) F = 7 N
Use the simulator!
1)
2)
3)
4)
5)
How do the spring constants of spring 1 and spring 2 compare?
Calculate the spring constant for spring 1.
Calculate the spring constant for spring 3.
Predict how far the spring will stretch with a 250 g weight.
Determine the weight of each cylinder.
Calculating period
In pendulums …
In springs …
m
NOTE: T = 2π
k
Period is NOT affected by
the amplitude of motion!
Period only depends on length &
gravity
 Longer string = longer period
 Weaker gravity = longer
period

Period only depends on mass
and spring constant.
 Higher mass = longer
period
 Looser spring / smaller
k = longer period

Period CFUs – Turn & Talk
1) If you stretch and release a slinky, you will notice that the
amplitude of its motion decreases over time (why?). How does
this decrease in amplitude affect the period of motion?
It doesn’t! Amplitude of motion does NOT affect
period.
2) Will a grandfather clock run slower or faster if placed on the
moon? Why?
The grandfather clock will run slow (have a longer
period) because as acceleration due to gravity
decreases, the period increases.
3) How does doubling the mass affect the period of a pendulum?
How does doubling the mass affect the period of a spring?
Doubling the mass has NO affect on the period of a
pendulum.
Doubling the mass of a spring increases the period
by a factor of √2
Conservation of energy
Ideally, pendulums and springs both conserve energy. (Realistically, they
lose energy over time due to friction).
In both cases, PE is maximum at maximum displacement. PE gradually
converts to KE, and reaches zero at the equilibrium point.
We have a simple formula for
KE shows the opposite trend
– it is
at equilibrium and reaches
the PE
inmaximum
a spring.
zero at maximum displacement.
In pendulums …
TE
In 2springs …
PEspring = ½ kx
Conservation of energy CFU
A and G have equal heights.
D is equilibrium position
Fill in the following table:
Position
PE (J)
KE (J)
A
50
0
B
35
C
15
D
G
You Do Problems 1) A spring stretches by 18 cm when a bag of potatoes weighing
56 N is suspended from its end.
a)
Determine the spring constant, k
b)
How much EPE does the spring have when it is stretched
this far?
You Do Problems 2) A pendulum swings from its release point, past equilibrium, to
its highest point on the opposite side in 0.4 seconds. The highest
point is 8 degrees above equilibrium. What is its frequency? Its
period? Its amplitude?
Frequency = 1 per 0.8 sec = 1.25 Hz
Period = 1/frequency = 1.6 s
Amplitude = 8o
3) You need to know the height of a tower but darkness obscures
the ceiling. You note that a pendulum extending from the ceiling
almost touches the floor and that its period is 12 s. How tall is
the tower?
T=
𝐿
2π√𝑔
𝑇√𝑔
=L
2π
L = 36 m
4) Billie releases the bob of his pendulum at an angle of 10° from
the vertical. At the same time, Bobby releases the bob of his
pendulum at an angle of 20° from the vertical. The two
pendulums have the same length. Does Billie’s bob reach the
vertical position before, after, or at the same time as Bobby’s bob?
Explain.
Same time. Amplitude does not affect period.
Damping and Resonance
Damping is the decrease in amplitude of a wave.
All real pendulums and springs have damping.
• Energy is lost due to friction
• Amplitude of motion becomes smaller, until it ceases
Some systems are designed to heavily damped, such as
 shock absorbers on a car
 Damping mechanisms in the foundations of buildings in
earthquake zones
Heavy
damping