Experimental Physics EP1 MECHANICS - The Laws of Motion · Experimental Physics - Mechanics - The...
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Experimental Physics - Mechanics - The Laws of Motion 1 Experimental Physics EP1 MECHANICS - The Laws of Motion - Rustem Valiullin https://bloch.physgeo.uni - leipzig.de/amr/
Transcript of Experimental Physics EP1 MECHANICS - The Laws of Motion · Experimental Physics - Mechanics - The...
Experimental Physics - Mechanics - The Laws of Motion 1
Experimental Physics EP1 MECHANICS
- The Laws of Motion -
Rustem Valiullin
https://bloch.physgeo.uni-leipzig.de/amr/
Experimental Physics - Mechanics - The Laws of Motion 2
From Kinematics to Dynamics
1 2
"⃗# "⃗$ = 0
Experimental Physics - Mechanics - The Laws of Motion 3
Newton’s First Law
An object continues to be in rest or continues its motion with a constant velocity unless it is acted on by an unbalanced force.
å == 0FFnet!!
å ¹= 0FFnet!!
Inertial reference system; law of inertia
Experimental Physics - Mechanics - The Laws of Motion 4
Newton’s Second Law
The acceleration ! of an object is inversely proportional to its mass " and is directly proportional to the acting force #.
mFa net /!!
= amFnet!!
=
- defines force:
The force required to produce an acceleration of 1 m/s2 is defined to be 1 newton (N).
- defines mass:
Mass is a measure of the resistance to acceleration.
1 N = 1 kg m / s2
2
1
2
1
aa
mm
=
Experimental Physics - Mechanics - The Laws of Motion 5
Hooke’s law
)( 0xxkF --=
k is the force constant of the spring
0x
F is negative
F is positive
Experimental Physics - Mechanics - The Laws of Motion 6
Switch activation force testing
How to measure forces
1F!
2F!
1F!
2F!
21 FFF!!!
+=
Experimental Physics - Mechanics - The Laws of Motion 7
Weight
gmFg!!
= The weight W of a body is a net force requiringto prevent the body from falling freely.
0=- gFW
gFW =
gF!
W!
v Can your apparent weight be greater than the true weight?
v How the mass and the weight of an astronautchanges far away of galaxies?
Experimental Physics - Mechanics - The Laws of Motion 8
Newton’s Third Law
Forces always occur in pairs. That means that if an object A exerts a force on another object B, then B will exert equal but opposite force on A.
Action-reaction pairs: law of interaction
Can the action and reaction forces balanceeach other?
No. They are acting on different objects!
W!
'W!
F!
'F!
Experimental Physics - Mechanics - The Laws of Motion 9
Ø The fundamentals of classical mechanics are
contained in three Newton’s laws of motion.
Ø Reference frames where the Newton’s laws are
applicable are called inertial reference frames.
Ø The Newton’s second law may be considered as a
definition of force and mass.
Ø The weight of an object is the gravitational
force between the object and the Earth.
Ø There are only four fundamental forces.
To remember!
Experimental Physics - Mechanics - The Laws of Motion 2 10
General scheme to solve problems
1. Isolate the object or the objects of interest.2. Draw detailed diagram of all external forces acting on the object.3. Choose a convenient coordinate system.4. Write down the second Newton’s law in the component form.5. Solve the resulting system of equations for the unknown quantity.6. Check yourselves (by considering extreme cases).
gmWFg!!!
==
T!
nF!
y
x
å == xx maTF
å =+-= 0ny FmgF
Experimental Physics - Mechanics - The Laws of Motion 2 11
Inclined surface
q
m
W!
nF!
y
x
å = xx maF
å = 0yF
q
gmW !!=
!" sin & = !()() = " sin &
*+ − !" cos & = 0&
&0sin&0 cos &
Experimental Physics - Mechanics - The Laws of Motion 2 12
Attwood’s Machine
m1
m2
T
gm1
T
gm2
å = yy maF
amgmT 11 =-
amgmT 22 -=-
12
12
mmmmga
+-
=
12
122mmmmgT+
=
Experimental Physics - Mechanics - The Laws of Motion 2 13
Multi-pulley system
å = 0yF
WT =5
WTT =+ 32
4321 TTTT =++
231 TTT ==
2/WF =
W!
Experimental Physics - Mechanics - The Laws of Motion 2 14
Static friction
F!
sf!
nss Ff µ=max,
nF!
totA
NFNfNFF n
n
N
iinn ´=´==å
=1,
nss Ff µ£areafs µmax, ×
Experimental Physics - Mechanics - The Laws of Motion 2 15
Kinetic friction
nkk Ff µ=F!
kf!
nF!
v! Experimental observations:• µk < µs
•µk does not depend on the area
• µk nearly constant for speeds between 1 cm/s and 10 m/sf
Ffs =
max,sf
kf
* How do wheels work?
Experimental Physics - Mechanics - The Laws of Motion 2 16
Inclined surface with friction
q
m
W!
nF!
y
x
q
gmW !!=
sf!
å = xx maF
å = 0yF
!
!
"# sin ! − () = 0
,- −"# cos ! = 0,- tan !2 − 3),- = 0
"# sin ! − (4 = "5656 = # sin ! − 34 cos !
7 sin !7 cos !
Experimental Physics - Mechanics - The Laws of Motion 2 17
Drag forces
W!
D
A – effective cross-sectionCD – geometric shape factorr - medium (fluid) density
! = 12%&'()
* ! −,- = ,.
)/0123456 =2,-%&'(
Experimental Physics - Mechanics - The Laws of Motion 2 18
Centrifugal force
v
T!a!
v
T!
r̂2
rmvFp =
!
1a!
amF !!=
pF!
Experimental Physics - Mechanics - The Laws of Motion 2 19
Coriolis force
v
v
Experimental Physics - Mechanics - The Laws of Motion 2 20
Coriolis force
v
v
Experimental Physics - Mechanics - The Laws of Motion 2 21
Ø To solve the problem, identify the object of interest
and all forces acting on, find a convenient coordinate
system, and finally apply the Newton’s second low in the
component form.
Ø Two bodies in contact may exert frictional forces on
each other.
Ø A fluid surrounding moving objects
may exert drag forces.
Ø There are pseudo-forces (centrifugal).
To remember!
