L3 DYNAMICS [tryb zgodnoÅ ci] - if.pwr.edu.plmmulak/PHYSICS 2019/Lecture3.pdf · 3k\vlfv '\qdplfv...
Transcript of L3 DYNAMICS [tryb zgodnoÅ ci] - if.pwr.edu.plmmulak/PHYSICS 2019/Lecture3.pdf · 3k\vlfv '\qdplfv...
Physics Dynamics
M. Mulak WUST 1
LAWS OF DYNAMICS
In classical mechanics we deal with objects that:- are large compared to the dimension
of atoms- move at speeds much less than the speed
of light
1010 m
83 10 /m s
Classical mechanics considers force to be a vectorquantity whose origin arises from a material body;(irrespective of the true nature of a force)
In general: ( , , )F r v t
Causes of motion concepts of force and massused to describe the change in motion of a particle
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Classification of forces
microscopic level:contact forces = repulsive electrical forces
(field forces)
* Michael Faraday (1791-1867)
macroscopic approach
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Four fundamental types of interaction
Interaction Source Relative Strength
Range
Gravitationalan attractive force between all particles (e.g. holds planets in their orbits around the sun)
Mass 10-38 Infinite
Electromagneticchemical reactions, light, radio, X rays, friction!
Electric charge
10-2 Infinite
Weak (Słabe)between quarks and leptons; associated with radioactivity
All elementa
ry particles
10-6 Short
10-18 m
Strong (Jądrowe)holds particles within the nucleus; the strong interaction between quarks and most other subnuclear particles
Hadrons (protons, neutrons, mesons) 1
Short
10-15 m
more basic electroweak interaction (1983)
progress in attempts to combine the strong & electroweak interactions in a singleGround Unified Theory
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Ancient „Natural Philosophy”(prior to Newton)
REST as a very specified, natural, state of bodies! &Uniform motion demands a force!
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The law of INERTIA
Each body continues in its state of rest or ofuniform motion in a straight line unless it iscompelled to change that state by forceimpressed upon it.
a tendency to resist any change in the state of motion
*New concept: force (not defined yet)
the class of uniform motions (Galileo)
before: an absolute rest distinguished! (Aristotle)
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Newton’s First Law
Inertial frames of reference exist.
A reference frame in which Newton’s FirstLaw is valid.
An unaccelerated reference frame: 0a
Any reference frame that moves withconstant relative to an inertial frame isitself an inertial one.
v
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Isaac Newton (1643-1727)
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the Earth?
a
toward the Sun:
toward the center of the Earth:a
3 24.4 10 /m s
2 23.4 10 /m s
Small comapared to 210 /g m s
In practice the Earth may be taken as the inertial reference frame.
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Foucault’s Pendulum
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Pantheon, Paris, 1852
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Newton’s Second Law
Concept of mass (m): measure of inertia, a standard has to be introduced (e.g. kilogram)
Once the standard of a unit of mass is chosen the Second Newton’s Law may serve to define force: it is defined by acceleration.
In SI units: 1 Newton (N) is a unit of force: acting on a particle of 1kg mass produces acceleration of 1m/s2
In an inertial reference frame the relationship between the net force acting on a body and the acceleration at which the body moves is given by:
F
a
F ma
the equation of motion (3 scalar equations)
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weightvs.
mass
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Constant force
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Classical mechanics is
fully deterministic
( , v, )F r t ma
+initial conditions
the future and the past are
precisely defined!
we can always find the trajectory of motion17 18
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Newton’s third law
If two bodies interact, the force exerted on body 1 by body 2 is equal to and opposite the force exerted on body 2 by body 1.
The action force is equal in magnitude to the reaction force and opposite in direction
but
they act on different bodies!
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on on B A A BF F
Action force
Reaction force
Forces always occur in pairs or
a single isolated force cannot exist
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ExampleAn apple pulls the Earth just as hard as theEarth pulls the apple. It seems however that onlythe apple is affected by the force of gravity(because when dropped it falls on the Earthrather then the Earth on the apple).Why?
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Applying Newton’s Laws to a body we are interested only in those external forces that act on the body. Here:
, n w
Action and reaction forces
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The forces exerted by the cart and by thehorse on each other are internal to the cart-horse system. They cannot affect themotion of the system as a whole. Thesystem moves forward because the forceexerted on the horse by the road is greaterthan the force exerted on the cart by theroad.
A "cart-horse" paradox: the harder thehorse pulls forward, the harder the cart willpull backward.
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Two masses placed in contact with each other on a frictionless, horizontal surface
1 2 F P m a P m a
EXAMPLES
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Free-body diagrams
1 2 F Q m a P Q m a
1 2 2 T f m a T w m a 30
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gmFw 1
NF
f
amfFF Nw
mamgmg )cos()sin(
)cos()sin( ga
Problem solving strategy Example: sliding down an incline
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The unequal masses are attached by a lightweight string that passes over a frictionless pulley of negligible mass.
frictionless incline
1 1 1
0
x
y
F
F T m g m a T m g
2 2
2
2 12 1
1 2
1 2
1 2
sin
sin 0
sin0 if sin
(1 sin )
x
y
F m g T m a
F n m g
m g m ga m m
m m
m m gT
m m
1m
2m
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m2m3 F23
f2f3
Fw2
Fw3
FAPm1F12
f1Fw1
FN1FN2FN3
F21F32
Y
amfFFFF NwAP
111211
Free-body diagram
FAPm1F12
f1
Fw1
FN1
Problem solving strategy Example: ‘a train’
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amfFFF
amfFFFF
amfFFFF
Nw
Nw
NwAP
333332
22232221
111211
amfF
amfFF
amfFFAP
3323
222312
1112
321321 mmmafffFAP
3223
2112
33
22
11
FF
FF
FF
FF
FF
Nw
Nw
Nw
gmf
gmf
gmf
333
222
111
321
321
mmm
fffFa AP
3323
1112
famF
fFamF AP
m2m3 F23
f2f3
Fw2
Fw3
FAPm1F12
f1Fw1
FN1FN2FN3
F21F32
Y
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Force of friction
s s k kf n f n
is nearly independent of the area of contact bewteen the surfaces
s
kcoefficient of static friction
coefficient of kinetic friction
n magnitude of the normal force
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FAP
FW=mg
f= FN
FN= FW
FAP
f
stick-slipNss Ff Nkk Ff
Example:Sound generation in a violin (with a bow) uses the difference between static and kinetic friction (stick-slip region). Try to explain the effect.
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Basic facts:1. no fundamental theory 2. proportional to the load (force pressing the two
surfaces together)3. independent of the area of contact independent of
the speed4. two kinds: static (no relative motion of the
surfaces) and kinetic (usually lower value):
Force of friction
Approximate coefficients of friction:static kinetic
steel on steel 0.74 0.57 aluminum on steel 0.61 0.47glass on glass 0.94 0.4teflon on teflon 0.04 0.04teflon on steel 0.04 0.04rubber on concrete (dry) 1.0 0.8rubber on concrete (wet) 0.30 0.25
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