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
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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 :
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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
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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
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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
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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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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=
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