Transcript 14.02.10APWeek23SimpleHarmonicMotion

AP Physics
Monday 14.02.03
Standards:
apply the expression for period of
oscillation to the mass of a spring.
Objective: SWBAT find the period of SHM
applied to horizontal springs
Agenda
1. Warm Up
2. Wavelike Motion
3. Simple Harmonic Motion:
Springs
Warm Up
What is the spring constant of a
spring that is stretched 2cm by a
50g mass?
Homework
C#8
AP Physics
Tuesday 14.02.04
Standards: 3b,c apply the
expression for the period of a
simple pendulum.
Objective: SWBAT solve simple
pendulum problems.
Agenda
1. Warm Up
2. Review HW
3. Simple Pendulum Notes
4. C#9
Warm Up
The period of a spring-mass
system undergoing simple
harmonic motion is T. If the
amplitude of the spring-mass
system’s motion is doubled, the
period will be:
a)1/4T b) ½ T c) T d) 2T e) 4T
Homework
C#9
AP Physics
Wednesday 14.02.12
Standards: analyze problems for vertical
and horizontal oscillations of springs
Objective: SWBAT solve complex
problems involving simple harmonic
motion
Agenda
1. Warm Up
2. Review HW
3. Energy in Simple Harmonic
Motion.
4. Guided Practice FRQ
Warm Up
Find the length of a simple
pendulum on earth consisting
of a light string swinging at 20°
to the vertical with a 8 kg
bowling ball suspended from
the end of the string if the
period is 3 minutes
Homework
Begin 4 page SHM extension
worksheet
AP Physics
Thursday 14.02.06
Standards: analyze problems for vertical
and horizontal oscillations of springs
Objective: SWBAT solve complex
problems involving simple harmonic
motion
Warm Up
A spring with a spring constant of 2N/m is
attached to the ceiling of the classroom.
Hanging from the spring is a 1 kg mass.
How far will the spring’s new equilibrium
position be from its original position. How
much energy is stored in the spring at this
position?
Agenda
1. Pass out Warm Up Found in the black box.
(students know where it is)
2. Give Warm Up 7 min.
3. Give students answer xequilibrium=4.9m,
U=24J
4. Collect Warm up and put it in black box.
5. Hand out Oscillations Extension
Worksheet. Students will work the rest of
the period.
Homework
Oscillation Extension HW
Packet
AP Physics
Friday 14.02.10
Standards: analyze problems
for vertical and horizontal
oscillations of springs
Objective: SWBAT solve
complex problems involving
simple harmonic motion
Agenda
1.
Pass out Warm Up Found in the black box.
(students know where it is)
2.
Give Warm Up 8 min.
3.
Give students answer Δxextension=5.9m,
Δxcompress=3.9m
4.
Collect Warm up and put it in black box.
5.
Hand out Oscillations Extension Worksheet.
Students will work the rest of the period.
Warm Up
The 2 N/m spring with the 1 kg mass
hanging from it from yesterday engages in
simple harmonic motion when 20 J of
work is done on it in the downward
direction to give the motion an amplitude
of 1 m. a) What is the maximum
compression and extension of the spring
from its unstretched position. Hint: The
natural unstretched position refers to the spring’s
equilibrium position with no effects of gravity.
Homework
Oscillations Extension
Worksheet
Profile of Wavelike Motion
Amplitude-is the magnitude of the wave or how
high or intense the wave gets. For springs and
pendulum this is the height of the wave
A
m
p
l
i
t
u
d
e
w=√(k/m) is the angular frequency
or angular velocity of oscillating
mass.
y=Acos(wt)
y (m)
T=2π√(m/k) for a spring
T=2π√(l/g) for a pendulum
time (s)
T
Frequency: The number of oscillations per
second or f=1/T
C#8 Simple Harmonic Motion Springs
a. T=20s
f=?
b. T=?
f=80Hz
c. T=?
k=40 N/m
m=15kg
d. T=?
F=20 N
x=4m
k=?
m=15kg
w=?
f=?
1. (1) A hummingbird makes a humming sound with its wings, which
beat with a frequency of 90.0 Hz. Suppose a mass is attached to a
spring with a spring constant of 2.50x102N/m. How large is the
mass if its oscillation frequency is 3.00x10-2 times that of a
hummingbird’s wings?
2. (3) A double coconut can grow for 10 years and have a mass of 20.0
kg. If a 20.0 kg double coconut oscillates on a spring 42.7 times
each minute, which is the spring constant of the spring?
3. (5) Suppose a 2662 kg giant seal is placed on a scale and produces
a 20.0 cm compression. If the seal and spring system are set into
simple harmonic motion, what is the period of the oscillations?
Guided Practice
A large pearl was found in the Phillipines in 1934. Suppose the
pearl is placed on a spring scale whose spring constant is 362
N/m If the scale’s platform oscillates with a frequency of 1.20
Hz, what is the mass of the pearl?
m=6.37 kg
Simple Pendulum Guided Practice
Two friends in France use a pendulum hanging from the world’s
highest railroad bridge to exchange messages across a river.
One friend attaches a letter to the end of the pendulum and
releases it so that the pendulum swings across the river to the
other friend. the bridge is 130.0 m above the river. How much
time is needed for the letter to make one swing across the river?
Assume the river is 16.0 m wide.
t=11.4 s
C#9 Simple Harmonic Motion of a Simple Pendulum
a.
Givens
T=?
l=2m
g=9.8m/s2
b.
Givens
T=20 min
l=?
g=9.8m/s2
c.
Givens
T=200s
l=12m
g=?
1. (1) An earthworm found in Africa was 6.7 m long. If this
worm were a simple pendulum, what would its period be?
2. (3) If bamboo, which can grow 88 cm in a day, is grown for
four days and used to make a simple pendulum, what will be
the pendulum’s period?
3. (6) Ganymede, the largest of Jupiter’s moons, is also the
largst satellite in the solar system. Find the acceleration of
gravity on Ganymede if a simple pendulum with a length of
1.00 m has a period of 10.5 s.
Guided Practice
• 1983B2. A block of mass M is resting on a horizontal, frictionless table and is attached
as shown above to a relaxed spring of spring constant k. A second block of mass 2M
and initial speed vo collides with and sticks to the first block Develop expressions for
the following quantities in terms of M, k, and vo
• a. v, the speed of the blocks immediately after impact
• b. x, the maximum distance the spring is compressed
• c. T, the period of the subsequent simple harmonic motion