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Class presentation slides for Physical Science 50 (second quarter) Spring Semester 2009
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Aristotle
Natural Motion
Galileo
Experimentation
Newton
Newton’s Laws of Motion, Gravity
Linear Motion
distanceSPEED = time
Linear Motion
displacementVELOCITY = time
Earth -> Sun
distance 1.497 x 1011 m
Time = velocity = 3 x 108 m/s
= 498.9 seconds
= 8.3 minutes
Sun -> Mars
d 2.28 x 1011 mt = v = 3 x 108 m/s
= 760.3 seconds
= 12.67 minutes
Acceleration
change in velocity
Acceleration = time
Deceleration
= Negative Acceleration
Saleen S7 Turbo
vf – vi 60 mph – 0 mph mpha = t = 3.3 s = 18.2 s
= 0.005 mi/s2
Gravitational Acceleration
Free Fall
Acceleration due to GRAVITY
Mass doesn’t matter
Gravitational Acceleration
Velocity increases at a constant rate
vf - vi
a = t 20m/s - 10 m/s
= 1 second
= 9.8 m/s2
= 32 ft/s2
Distance Fallen
Distance = Velocityaverage x time
vi + vf
= 2 x t0 + gt
= 2 x t
= 1/2 gt2
Transamerica Building
46 g golf ball droppedfrom top of Transamericabuilding
7.35 seconds to hit ground
d = ????
Transamerica Building
46 g golf ball droppedfrom top of Transamericabuilding
7.35 seconds to hit ground
d = 1/2gt2
= (0.5)(9.8 m/s2)(7.35s)2
= 265 m = 853 ft
g and elevation
ATT vs. Coors Field
sea level 5280 ft9.8185 m/s2 9.8136 m/s2
G force
Extreme Acceleration> 1g
Breathing difficultiesblackout
Gravity
Newton’s Laws of Motion
1) Every body continues in a state of rest or in uniform motion in a straight line unless compelled to change that state by forces impressed upon it.
INERTIA
Inertia
Newton’s Laws of Motion
2) The acceleration produced by a Force acting upon on body is directly proportional to the mass of the body.
F = m x a
Force Units
F = m x a = 2000 kg x 0.05 m/s2
= 100 kg m/s2 = 100 Newtons
Force of Gravity
F = m x a
Fg = m x g
Fg = WEIGHT
Mass vs. Weight
60 kg person
Weight = m x g
Earth Moon Jupiter(60 kg)(9.8m/s2) (60 kg)(1.67 m/s2) (60 kg)(25.9 m/s2)
588 N 100 N 1552 N
Weightlessness
“less” gravity
NOT
no gravity
Newton & Gravity
1687
Principia
“Every object in the universe is attracted toand attracts every other
object in the universe by a force called gravity”
Gravitational Force
Mutually attractive force
Inverse square
GM1M2 Fg = r2 where G = 6.67 x 10-11Nm2/kg2
g on Uranus?
Fg = m x g = GM1M2/r2
G Mplanet
g = rplanet2
(6.67 x 10-11 Nm2/kg2)(8.44 x 1025 kg)g = (2.56 x 107 m)2
g = 8.59 m/s2
Size of Gravitational Force
(6.67 x 10-11 Nm2/kg2) (60 kg)(60 kg)Fg = (1 m)2
Fg = 2.4 x 10-7 N
Size of Gravitational Force
(6.67 x 10-11 Nm2/kg2) (6 x 1024 kg)(7.35 x 1022kg)
Fg = (3.83 x 108 m)2
Fg = 2 x 1020 N
Escape Velocity
d = 1/2gt2 for objects in free fall
2d = gt2 but t = v/g for free fall
2d/g = t2 = (v/g)2
2 dg = v2
√2dg = v = ESCAPE VELOCITY
Escape Velocity
vE = √2dg
= √2gREarth
= √2(9.8m/s2)(6.378 x 106 m)
= 11.18 X 103 m/s
How high will it go?
V2 = 2dg
V2/2g = d
(10 m/s)2
2 (9.8 m/s2) = d
d = 5.1 m
Newton’s Laws of Motion
In the absence of outside forces, the total momentum of a set of objects remains the same no matter how the objects interact with one another.
p = m v
Conservation of Momentum
m vbefore = m vafter
(3000 kg)(10m/s) + (1000 kg)(0 m/s) = (3000 kg)v’ + (1000 kg) (15 m/s)
30,000 kg m/s = (3000 kg) v’ + 15,000 kg m/s
15,000 kg m/s = (3000 kg) v’ -------> v’ = 5 m/s
Conservation of Momentum
m vbefore = m vafter
(2000 kg) (8 m/s) + (50 kg) (0 m/s) = (2000 + 50 kg) v’
16,000 kg m/s ÷ 2050 kg = v’ = 7.8 m/s
Inelastic Collisions
(2 kg)(10 m/s) 3 kg
v = 0 m/s v’ =?
Elastic Collisions
(2 kg)(10 m/s) 3 kg
v = -2 m/s v’ =?
Angular Momentum
m1 x v1 x r1 = m2 x v2 x r2
Circular Motion
2 r = diameter
2πr = circumference
Magnitude of v doesn’tchange but directiondoes
Centripetal Acceleration
va = t
vt - vb
= 1/2(2r)/v 2v
= r/v v2 mv2
ac = r Fc = r
Applications
Spin cyclewasher
Car turning
The ROTOR
Centripetal Force
mball = 0.25 kg
r = 0.5 m
v = 2 m/s
Fc = ?
Centripetal Force
mball = 0.25 kg
r = 0.5 m
v = 2 m/s (0.25 kg)(2 m/s)2
Fc = 0.5 m
= 2 Newtons
Roller Coaster Loop
Fc > Fg
mv2 r > mg
V2/r > g
Conservation of Energy
The Energy of the UniverseIs neither created nor destroyed;It merely changes form.
Forms of Energy
Work and Power
W = F x d
workPower = time
Work
W = F x d
W = m x g x d
W = (50 kg)(9.8m/s2)(5m)
= 2450 kg m2/s2
= 2450 Joules
Power
Work Power = time
2450 J = 30 s
= 81.67 J/s
= 81.67 Watts
Kinetic Energy
Work = F x d = (m x a) x d
If d = 1/2at2 and v = atthen d = 1/2a(v/a)2 = 1/2v2/a
W = m a d = m a (1/2 av2/a) = 1/2mv2
Potential Energy
Potential Energy = m x g x h
Potential & Kinetic Energy
PE + KE = Total Energy
PEtop = KEbottom
mgh = 1/2mv2
2gh = v2
V = √2gh
Escape Velocity
vE = √2dg
= √2gREarth
= √2(9.8m/s2)(6.378 x 106 m)
= 11.18 X 103 m/s
Terminal Velocity
1 Kg book falls 1 meter
vf = ?
V = √2gh
= √2(9.8m/s2)(1m)
= √19.6 m2/s2 = 4.4 m/s
How tall is the incline?
V = 5.42 m/s
V = √2ghThus h = v2/2g
= (5.42 m/s)2/2(9.8 m/s2)
= 1.5 m
Roller Coaster
Pole Vault
World Record = 6 m
V = √2gh
= √2 (9.8m/s2)(6 m)
= 10.9 m/s
Heat transfer
Heat:Energytransferred between2 systems in contactand at different temperatures
Temperature
Average kinetic energyof atoms or molecules
Temperature scales
Biological Temperature Regulation
Human: 37C = 98.6 F
Shivering, flushing
Biological Temperature Regulation
Birds
Animal fat layer
Specific Heat
The Amount of heat energy necessary to raise the temperatureof a given substance
Heat Energy Q
Q = m C T
C in units of Joules/g °C or
calories/g °C
Heat Energy
Heat Capacity C
Calories
1 calorie: amount of heat neededto raise tempof 1.0 gram
H2O 1° C
Dietary Calories
1 Calorie = 1000 calories
100 Calories100,000 calories!
Calorie burning
Heat Transfer
Wooden vs. Aluminum
Each pot contains 500 cal.
Each spoon 100 g
How hot will each one get?
Heat Transfer
Aluminum spoon
Q = mCT = 500 cal = (100g)(0.22cal/gºC) T
500 calT = (100g) (0.22cal/gºC)
= 22.73°C
Heat Transfer
Wooden spoon
Q = mCT = 500 cal = (100g)(0.58cal/gºC) T
500 calT = (100g) (0.58cal/gºC)
= 8.82°C
Identifying Unknowns
A 400 g metalw/3680 Joules of HeatTemp 50°C -> 60°C
What is C?Q
C = mT
= 3680 J/400g (10°C)
= 0.92 J/g °C
Limiting Heat Transfer
Cair = 0.17 cal/g°C
Refrigeration
Sound Energy
Result of Vibrations
Air molecules disturbed
Ear membrane vibration
Auditory nerve -> Brain
Hearing
Cochlea
Waves
Wavelength: distancebetween crests()
Frequency: # crestspass a given pt/time (f)
x f = velocity of sound(m) (1/sec)
1/sec = HERTZ
Infrasound
f of elephant communicationif is 34 m?
f x = vs = 340 m/s
vs
Thus f = = 10 1/s = 10 Hz
Ultrasound
f of dolphin communicationif is 0.0034 m?
f x = vs = 340 m/s
vs
Thus f = = 105 Hz
Audible Sound Waves
Hearing range fornormal human:20 - 20,000 Hz
S,z,c soundsvs.
M,b sounds
Sound & Medium
0º C air 331 m/s
Helium gas 970 m/s
Fresh water 1493 m/s
Salt water 1513 m/s
Granite 6000 m/s
Velocity of sound in different media
Sound & Temperature
vs = vo + (0.61 m/sºC)T
Hot Day vs. Cold Day
110° F vs. –30 ° F?
At 110° F = 43.33 °Cvs = 331 m/s + (0.61m/s °C) (43.3 °C)
= 357.43 m/s
At –30 ° F = –34.4 ° Cvs = 331 m/s + (0.61m/s °C) (–34.4 ° C) = 310 m/s
Echolocation
Bat sends signal and receives echo 0.7 slater in 4° C cave --how far is the wall?
vs = 331 m/s + (0.61m/s °C) (4°C) =333.4m/s
d = v x t = vs x t/2 = (333.4m/s)(0.35s) =116.7 m
Sound Intensity
Bel = 10 db
intensity doubling
(d2)2 I1
(d1)2 = I2
Intensity drops with (distance)2
Sound Intensity
Intensity comparison
Standing 2 m vs. 200 m from jet taking off?
(200m)2 120 db (2 m)2 x
40000/4 = 105 = 5 factors of 10
x = 70 db
Doppler Effect
Doppler Effect
Approaching sound f Vs
f’ = f VS - V
Retreating sounds f
Vs
f’ = f VS + V
Doppler Example
Approaching at 30m/s:340m/s
f’ = (440 Hz) 340 - 30 m/s = 483 Hz
Retreating at 30 m/s:340m/s
f’ = (440 Hz) 340 + 30 m/s = 404 Hz
Medical Doppler
Blood flow velocityF= 80000 Hz, f’ = 80020 Hz
f’ vs 1500 m/sf = vs - v = 1.00025 = 1500 - v m/s => v = 0.375 m/s = 37.5 cm/s
Sonic Boom
Music
PythagorasOctave = 2 fHarmonious frequencies = simpler ratio