phys16 – lecture 32
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PHYS16 – Lecture 32. Simple Harmonic Motion November 29, 2010. Exam Answers. Question 1 – Lift of Plane. Use Bernoulli to calculate lift Use Newton’s laws. Question 2 – Height of sky and ocean . Height of sky given constant density Height of sky given that density changes - PowerPoint PPT PresentationTRANSCRIPT
PHYS16 – Lecture 32
Simple Harmonic Motion November 29, 2010
Exam Answers
Question 1 – Lift of Plane
• Use Bernoulli to calculate lift
• Use Newton’s laws
MN 28.645 ),(
2 ),(2 22
wingone
F
vvvvPPAF bottopbottop
MN 25.4
)sin()sin()sin(
FdtdVv
dtdmvmv
dtd
dtdpF
Question 2 – Height of sky and ocean
• Height of sky given constant density
• Height of sky given that density changes
• Height of ocean given constant density
km 9.7
gPh
km 18 ,00 /
0
hePP Pgh
km 1.11
gPh
Question 3 – Car performance
• Power of car
• Torque of car (4 wheels)
kW 220
))sin(
P
mgFFFvP
friction
Nm 2600or /
FrP
Question 3 – Car performance
• Rpm of engine
• Torque on wheelsrpm 11000 1st rpm, 6300 2nd
rpm 42003rd rpm, 32004th rpm, 2400 5th
wheeldiffgearengine GRGR
Nm 4500 1st Nm, 6002 2ndNm 14003rd Nm, 8804th Nm, 550 5th
enginediffgearwheels GRGR
Question 4 – Answer is 42
• Time for ball to tunnel through Earth
• Distance to geostationary orbit
min 424
334
E
E
Gt
mrGF
Earth ofcenter thefrom Mm 42
4 2
3
2
rGMr
T
E
Question 4 – Answer is 42
• Time for low orbit satellite to go ½ around Earth
• Height of object on Ganymede
km 4221
281
2
hhR
GMR
GMv
RGMv
initial
initial
min 422
4 2
3
2
TtGMR
T
EE
Question 5 – Swing set
• John jumps on Merry-go-round
• Balancing multiperson see-saw
m 6-at kg 50 and 2m,at kg 35 m, 4at kg 20 m, 6at kg 25044332211 xmxmxmxm
rad/s 33.2
Johnmerry
JohnmerryJohnmerrymerryJohnmerrymerry IrpI
Question 5 – Swing set
• Mass of kid on tippy bridge
kg 5.250)sin()cos(
0)cos()sin(
0
21
21
2
mTT
TTmgMgTplank
Outline for Oscillations
• Simple Harmonic Motion– Position, Velocity, Acceleration– Force– Energy
• Waves– Mechanical waves– Intensity and Power– Superposition and Interference– Standing Waves
Simple Harmonic Motion:Position, Velocity, Acceleration
Oscillations and Periodic Motion
http://img.tfd.com/ggse/c9/gsed_0001_0012_0_img2993.png
Simple Harmonic Motion
T
tAx
2
)sin(
Equilibrium Point
1) About Equilibrium2) Periodic3) Sinusoidal
http://www.gailruby.com/Picture4.png
Examples
• Mass on a Spring• Pendulum
• Snowboarder in halfpipe• Bungee jumper• Child on swing• Bobble head doll?
SHM Position, Velocity, Acceleration
http://www.tutornext.com/system/files/u89/Chapter%2011-3.gif
)sin(
)cos(
)sin(
2 tAa
tAv
tAx
Example Question
• What is the max speed and when does it occur?
Equilibrium Point
Tat 0T/2at max
vAv
Example Question
• An object undergoes simple harmonic motion. If the amplitude and period are doubled, the object’s max speed is:
A) QuadrupledB) DoubledC) UnchangedD) HalvedE) Quartered
Simple Harmonic Motion:Restoring Force
Restoring Force
• Force that always points back to the equilibrium position
k is just a constant – for a spring it is the spring constant
xkxF ˆ
http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/images/gif/spring_mass_dia.gif
SHM – Restoring Force
mkf
mk
xmkx
tAmtAk
xkxF
21 ,
)sin()sin(dtdmma
2
2
2
2
Example Question
• A block on a spring has a period of T. What is the period if:
A) the mass is doubled?
B) k is quadrupled?
C) A is doubled?
T2
T21
T
Example Question• What is the period of a pendulum?
http://upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pendulum.png/300px-Pendulum.png
Lg
smallfor ,
)sin(
Lsmgks
mgksF
Simple Harmonic Motion:Energy
Energy in SHM
2
22222
22
21
)(cos21)(sin
21
21
21
kAE
tAktAmE
kxmvE
http://www.farraguttn.com/science/milligan/APPhys/SHMOver_files/image022.jpg
Main Points - SHM
• Movement
• Restoring Force creates oscillation
• Energy is dependent on amplitude
)sin( tAx
2
2
dtxdmkxF
2
21 kAE