Transcript Chapter 4

Chapter 4
The Laws of 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 –
they will add as vectors
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 4
Problem 12
Two forces are applied to a car in an effort to move it. (a) What is the resultant
of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration
does it have? Ignore friction.
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


F12   F21
Forces of different origins
• Gravitational force
• Normal force
• Tension force
• Frictional force (friction)
• Drag force
• Spring force
Gravity force (a bit of Ch. 7)
• 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
Normal force
• When the body presses against the surface
(support), the surface deforms and pushes on the
body with a normal force (n) that is perpendicular to
the surface
• The nature of the normal force – reaction of the
molecules and atoms to the deformation of material
Normal force
• The normal force is not always equal to the
gravitational force of the object
Free-body diagrams
Free-body diagrams
Chapter 4
Problem 30
An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is
connected to a cable that passes over a pulley and is then fastened to a
hanging object with mass m2 = 10.0 kg, as shown in the Figure. Find the
acceleration of each object and the tension in the cable.
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 n
• Coefficient of kinetic friction μk
f k  k n
• 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 4
Problem 49
Find the acceleration reached by each of the two objects shown in the figure if
the coefficient of kinetic friction between the 7.00-kg object and the plane is
0.250.
Answers to the even-numbered problems
Chapter 4
Problem 2
25 N
Answers to the even-numbered problems
Chapter 4
Problem 6
7.4 min
Answers to the even-numbered problems
Chapter 4
Problem 26
4.43 m/s2 up the incline, 53.7 N
Answers to the even-numbered problems
Chapter 4
Problem 40
(a) 55.2°;
(b) 167 N
Answers to the even-numbered problems
Chapter 4
Problem 50
(a) 18.5 N;
(b) 25.8 N