m01 principles

8/12/2019 M01 Principles

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- PHYSICAL QUANTITIES and DIMENSIONS- MEASURE UNITY SYSTEMS- SCALARS E VECTORS- DISPLACEMENT, VELOCITY, ACCELERATION- DYNAMICS PRINCIPLES- GRAVITY- MASS, WEIGHT, DENSITY, FLOW, PRESSURE

MECHANICSIst part

D. SCANNICCHIO 2009

corso integrato FISICA - disciplina FISICA

Corso di Laurea Specialistica inMEDICINA e CHIRURGIA

Laurea Magistralis in MEDICINE and SURGERY

Integrated Course/Discipline: PHYSICS

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HARVEY


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STATICS

KINEMATICSDYNAMICS

BASIC

MECHANICS

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PHYSICAL QUANTITIES

definition measurable

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DIMENSIONS

fundamental [L] lenght [M] mass [t] time [i] electric current

derived [L]a[M]b[t]c[i]d

dimensional equations:

control of physical relations uniformity

FUNDAMENTAL CONSTANTS

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UNITS of MEASUREMENT SYSTEMS

International System (S.I.)(previous MKSQ System)

meter (m) kilogram (kg) second (s) ampere(A)

C.G.S. System

centimeter (cm) gram (g) second (s)

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Practical Systems examples:

millimeter of mercury (mmHg) atmosphere (atm)hour (h) ngstrom() electronvolt(eV) ..............

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deci- (d)

centi- (c)

milli- (m)

micro- ()pico- (p)

sottomultiplimultipli

tera- (T)

giga- (G)

mega- (M)

kilo- (k)

1012

109

106

103

peta- (P) 1015

101

102

103

106

1012

nano- (n) 109

MULTIPLES and SUBMULTIPLE

multiplessubmultiples



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SCALAR QUANTITIES

characterization: only 1number(ratio between the physical quantity and its measuring unit)

examples

mass m = 73.8 kg time t = 32.3 s density d = m/V = 4.72 g cm3



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VECTOR QUANTITIES

characterization: 3data

modulus

direction

versus

application pointv

modulus

direction

versus

lettervin bold

examples: displacement svelocity v

s = 16.4 mv = 32.7 m s1

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DISPLACEMENT

displacementdifined with :modulus, direction, versus vector s

to

trajectory : a line tangent to the vector sin every pointand in every subsequent time instant with the following components:

s = s(t)x = x(t)y = y(t)z = z(t)

t1t2s1 s2

dimensions [L]

measure units: I.S. (meter (m)) C.G.S. (cm)



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VARIATION (CHANGE) DEFINITION of a PHYSICAL QUANTITY

distance variation s (in modulus):

(from initial value s1=23 m to final value s2=16 m) !s = 16 m 23 m = - 7 m (from initial value s1= 23 m to final value s2=16 m) !s = 16 m (23 m) = + 39 m

variat ion or change: a2 a1= afinal ainitial= !a

difference: a1 a2= ainitial afinal= !a

variat ion or change symbol : !



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SOME MOTION of BODIES

rectilinear uniform motion

rectilinear motion uniformly accelerated

circolar uniform motion

harmonic motion

rectilinear motion(same direction and versus) :

t1 s1 = s(t1 )t2 s2 = s(t2 )

!s= s2 s1= s(t2) s(t1)}



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VELOCITY

velocity = time intervalcovered distance


0x

y

z

t2

s1 s

1

s2

s2

t1t

0

vm

velocit media: vm= s(t

2) s(t1)t

2 t

1

=

st

t2 t

1

s2 s1

=mean velocity


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velocit media:

vm=

s(t2) s(t1)t

2 t

1

=

st

t2 t

1

s2 s1

=mean velocity

INSTANT VELOCITY

velocit istantanea: v = lim st

t 0=

d s(t)

dt

instant velocity

dimensions [v] = [L] [t]1

measure units: I.S. (m s1) C.G.S. (cm s1)



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ACCELERATION

a

m= v(t2) v(t1)

t2 t

1

=

vt

accelerazione media:mean acceleration :

a = lim vt

=d v(t)

dt

t 0accelerazione istantanea:instant acceleration :


dimensions [a] = [L] [t]2

measure units: I.S. (m s2) C.G.S. (cm s2)


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force"

physical quantity modifying the motioncondition of a body

motion condition of a body: defined by its velocity motion condition change "velocity vector change velocity vector change "acceleration vector

II- F =m a

mass m = amount of matter

DYNAMICS PRINCIPLES

I- INERTANCE PRINCIPLE in absence of forcesa body is at rest or move with rectilinear uniform motion

( v = constant in modulus, direction and versus)



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II- F =m a

DYNAMICS PRINCIPLES

dimensions [a] = [M] [L] [t]2measure units:

I.S. newton (N) = kg meter s2

C.G.S. dyne (dyn) = gram cm s2

1000 x 100 = 100 000 = 105

1 newton = 105 dynes



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DYNAMICS PRINCIPLES

III- ACTION-REACTION PRINCIPLE

BODY A BODY B

FAB = FBA

LINEAR MOMENTUM CONSERVATION

linear momentum definition: q = m v

!q = 0(isolated system)



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aA=

FAB

mA=

vA

t aB=FBA

mB=

vB

t

LINEAR MOMENTUM CONSERVATION

mAa

A + m

Ba

B= 0

mA v

A + m

B v

B= 0

FAB + FBA = 0(vectors with same direction and opposite versus)

qA+ q

B= 0 !q total = 0

(isolated system)D. SCANNICCHIO 2009 17/23


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G = 6.67 1011N m2kg2

(Newton)

F = G m1m2

r2r

r

m

1

m2

r

GRAVITATIONAL FORCE

at Earth ground : MTEarth mass RTEarth radius m mass of the body

F = G =gmMT m

R2

g= 9.8 m s2= 980 cm s2

F = mg= p

(definition of the gravity force vector p)D. SCANNICCHIO 2009 18/23


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p = gravity force vector

p

linee di forza

xy

z

suolo

90

ground

lines of forcemodulus p = mgdirection vertical

versus to ground

space domain where forces are actingFORCE FIELD


g= 9.8 m s2= 980 cm s2

F = mg= p

GRAVITY FORCE FIELD


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H2O d = 1 g cm3 = 1000 kg m3

m kg g

kggravity= kgmass9.8 m s2 = 9.8 N

gravity kggravity ggravity

MASS, GRAVITY, DENSITY

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d =m

V

[d] = [M][L]3

I.S. kg m3 C.G.S. g cm3

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FLUID FLOW

V

t

Q =Vt

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[Q] = [L]3[t]1

I.S. m3s1 C.G.S. cm3s1

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PRESSURE

p = FnS =F nS.

n

Fn

F

S

pascal = 105dine

104cm2 =10 barie

=[M][L]1[t]2[M][L][t]2

[L]2[p] =

I.S. N/m2 pascal (Pa)

C.G.S. dyne/cm2 barye



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1 atmosphere = 760 mmHg = 760 tor = 1.016 106barye == 1.016 10 pascal = 1033 ggravitycm2

(0C)

PRESSURE


hydrostatic pressure: p = d gh = = 13.59 g cm3980 cm s176 cm = 1.016 106barye


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RECTILINEAR UNIFORM MOTION and

MOTION with CONSTANT ACCELERATION

rectilinear uniform motion v= constant = vo s = vot + so so=initial displacement

motion with constant acceleration a= constant = ao v = aot + vo vo=initial velocity

s = aot2 + vot + sos

o=

initial displacement

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D. SCANNICCHIO 2009


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massima gittata per = 45

x

y

g

v

ox

v

oy

v

vox

vy

vo

vo

vox

voy

vox

v

vox

vy

vy = 0

o

body undergoing gravity accelerationg

maximum range for #= 45

BULLET MOTION

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vx= v

ox

vy= v

oy gt

g2 voytouchdown time t =


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a

aN

aT

aN

a

v

v

R

aT

x

y

o

CURVILINEAR MOTION

accelerazione tangenziale aT aT =dv

dt

accelerazione normale (radiale) aN

aN =

v2

R

radial acceleration (normal)

tangential acceleration

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KEPLERS LAWS

1st- The planets in their motion around the Sun describe an

elliptical orbit with the Sun in one of the ellipsis focuses.

3rd- The square of revolution times T are directly proportional

to the third power of the half longer orbital axis a:

T2

a3= constant

2nd- The area sweeped by the vector radiuses are directly

proportional to the times !t spent to be traced:

when S1= S2than !t1= !t2 from whichAB

!t1

CD

!t2< .

S1

!t

S2

!t=

D. SCANNICCHIO 2009

m01 principles

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