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

1

Classification of forces

microscopic level:contact forces = repulsive electrical forces

(field forces)

* Michael Faraday (1791-1867)

macroscopic approach

2

Physics Dynamics

M. Mulak WUST 2

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

3 4

Ancient „Natural Philosophy”(prior to Newton)

REST as a very specified, natural, state of bodies! &Uniform motion demands a force!

Physics Dynamics

M. Mulak WUST 3

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)

5 6

Physics Dynamics

M. Mulak WUST 4

7

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

8

Physics Dynamics

M. Mulak WUST 5

Isaac Newton (1643-1727)

9

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.

10

Physics Dynamics

M. Mulak WUST 6

Foucault’s Pendulum

11

Pantheon, Paris, 1852

12

Physics Dynamics

M. Mulak WUST 7

13

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)

14

Physics Dynamics

M. Mulak WUST 8

weightvs.

mass

15

Constant force

16

Physics Dynamics

M. Mulak WUST 9

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

Physics Dynamics

M. Mulak WUST 10

19 20

Physics Dynamics

M. Mulak WUST 11

21

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!

22

Physics Dynamics

M. Mulak WUST 12

on on B A A BF F

Action force

Reaction force

Forces always occur in pairs or

a single isolated force cannot exist

23

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?

24

Physics Dynamics

M. Mulak WUST 13

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

25

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.

26

Physics Dynamics

M. Mulak WUST 14

Two masses placed in contact with each other on a frictionless, horizontal surface

1 2 F P m a P m a

EXAMPLES

27 28

Physics Dynamics

M. Mulak WUST 15

29

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

Physics Dynamics

M. Mulak WUST 16

31 32

Physics Dynamics

M. Mulak WUST 17

gmFw 1

NF

f

amfFF Nw

mamgmg )cos()sin(

)cos()sin( ga

Problem solving strategy Example: sliding down an incline

33 34

Physics Dynamics

M. Mulak WUST 18

35

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

36

Physics Dynamics

M. Mulak WUST 19

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’

37

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

38

Physics Dynamics

M. Mulak WUST 20

39 40

Physics Dynamics

M. Mulak WUST 21

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

41

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.

42

Physics Dynamics

M. Mulak WUST 22

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

43 44