#### Transcript Chapters 5-6

```Chapters 5, 6
Force and Motion
Newtonian mechanics
Sir Isaac Newton
(1643 – 1727)
• Describes motion and interaction of objects
• Applicable for speeds much slower than the speed
of light
• Applicable on scales much greater than the atomic
scale
• Applicable for inertial reference frames – frames
that don’t accelerate themselves
Force
• What is a force?
• Colloquial understanding of a force – a push or a
pull
• Forces can have different nature
• Forces are vectors
• Several forces can act on a single object at a time –
Force superposition
• Forces applied to the same object are adding as
vectors – superposition
• The net force – a vector sum of all the forces applied
to the same object
Newton’s First Law
• If the net force on the body is zero, the body’s
acceleration is zero


Fnet  0  a  0
Newton’s Second Law
• If the net force on the body is not zero, the body’s
acceleration is not zero


Fnet  0  a  0
• Acceleration of the body is directly proportional to
the net force on the body
• The coefficient of proportionality is equal to the
mass (the amount of substance) of the object
 
ma  Fnet

 Fnet
a
m
Newton’s Second Law
• SI unit of force kg*m/s2 = N (Newton)
• Newton’s Second Law can be applied to all the
components separately
• To solve problems with Newton’s Second Law we
need to consider a free-body diagram
• If the system consists of more than one body, only
external forces acting on the system have to be
considered
• Forces acting between the bodies of the system are
internal and are not considered
Chapter 5
Problem 6
Newton’s Third Law
• When two bodies interact with each other, they exert
forces on each other
• The forces that interacting bodies exert on each
other, are equal in magnitude and opposite in
direction


FBC   FCB
Forces of different origins
• Gravitational force
• Normal force
• Tension force
• Frictional force (friction)
• Drag force
• Spring force
Gravity force (a bit of Ch. 13)
• Any two (or more) massive bodies attract each other
• Gravitational force (Newton's law of gravitation)

m1m2
F  G 2 rˆ
r
• Gravitational constant G = 6.67*10 –11 N*m2/kg2 =
6.67*10 –11 m3/(kg*s2) – universal constant
Gravity force at the surface of the Earth

mEarthmCrate ˆ
m1m2
FCrate  G 2 rˆ  G
j
2
r
REarth

 GmEarth 
mCrate ˆj  g mCrate ˆj
FCrate   2
 REarth 
g = 9.8 m/s2
Gravity force at the surface of the Earth
• The apple is attracted by the Earth
• According to the Newton’s Third Law, the Earth
should be attracted by the apple with the force of the
same magnitude

mEarthmApple
m1m2
ˆj
FEarth  G 2 rˆ  G
2
r
REarth

a Earth 
G
mEarthm Apple
2
Earth
R
mEarth
m Apple
 GmEarth  mApple ˆ
ˆj
ˆj  



g

j
 R2
m
mEarth
 Earth  Earth
Weight
• Weight (W) of a body is a force that the body exerts
on a support as a result of gravity pull from the Earth
• Weight at the surface of the Earth: W = mg
• While the mass of a body is a constant, the weight
may change under different circumstances
Tension force
• A weightless cord (string, rope, etc.) attached to the
object can pull the object
• The force of the pull is tension ( T )
• The tension is pointing away from the body
Free-body diagrams
Chapter 5
Problem 47
Normal force
• When the body presses against the surface
(support), the surface deforms and pushes on the
body with a normal force (FN) that is perpendicular to
the surface
• The nature of the normal force – reaction of the
molecules and atoms to the deformation of material
Free-body diagrams
Free-body diagrams
Chapter 5
Problem 41
Frictional force
• Friction ( f ) - resistance to the sliding attempt
• Direction of friction – opposite to the direction of
attempted sliding (along the surface)
• The origin of friction – bonding between the sliding
surfaces (microscopic cold-welding)
Static friction and kinetic friction
• Moving an object: static friction vs. kinetic
Friction coefficient
• Experiments show that friction is related to the
magnitude of the normal force
• Coefficient of static friction μs
f s ,max   s FN
• Coefficient of kinetic friction μk
f k  k FN
• Values of the friction coefficients depend on the
combination of surfaces in contact and their
conditions (experimentally determined)
Free-body diagrams
Free-body diagrams
Chapter 6
Problem 23
Drag force
• Fluid – a substance that can flow (gases, liquids)
• If there is a relative motion between a fluid and a
body in this fluid, the body experiences a resistance
(drag)
• Drag force (D)
D = ½CρAv2
• C - drag coefficient; ρ – fluid density; A – effective
cross-sectional area of the body (area of a crosssection taken perpendicular to the velocity); v - speed
Terminal velocity
• When objects falls in air, the drag force points
upward (resistance to motion)
• According to the Newton’s Second Law
ma = mg – D = mg – ½CρAv2
• As v grows, a decreases. At some point acceleration
becomes zero, and the speed value riches maximum
value – terminal speed
½CρAvt2 = mg
Terminal velocity
Solving ½CρAvt2 = mg we obtain
2mg
vt 
C A
vt = 300 km/h
vt = 10 km/h
Spring force
• Spring in the relaxed state
• Spring force (restoring force) acts to restore the
relaxed state from a deformed state
Hooke’s law
• For relatively small deformations


Fs  kd
Robert Hooke
(1635 – 1703)
• Spring force is proportional to the deformation and
opposite in direction
• k – spring constant
• Spring force is a variable force
• Hooke’s law can be applied not to springs only, but
to all elastic materials and objects
Centripetal force
• For an object in a uniform circular motion, the
centripetal acceleration is
2
v
ac 
R
• According to the Newton’s Second Law, a force
must cause this acceleration – centripetal force
mv
Fc  mac 
R
2
• A centripetal force accelerates a body by changing
the direction of the body’s velocity without changing
the speed
Centripetal force
• Centripetal forces may have different origins
• Gravitation can be a centripetal force
• Tension can be a centripetal force
• Etc.
Free-body diagram
Chapter 5:
Problem 2.
(a)1.88 N;
(b) 0.684 N;
(c) (1.88 N)ˆi + (0.684 N)ˆj
Chapter 5:
Problem 10.
(a)2.0N;
(b) down
Chapter 5:
Problem 22.
(a) 5.5 kN;
(b) 2.7 s;
(c) 4.0;
(d) 2.0
Chapter 6:
Problem 2.
0.61
Chapter 6:
Problem 32.
3.75
Chapter 6:
Problem 36.
48km/h