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