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Chapter 4
Forces and Newton’s 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
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
• 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

aEarth 
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 4
Problem 54
The steel I-beam in the drawing has a weight of 8.00 kN and is being lifted at a
constant velocity. What is the tension in each cable attached to its ends?
Normal force
• When the body presses against the surface
(support), the surface deforms and pushes on the
body with a normal force 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 61
The drawing shows box 1 resting on a table, with box 2 resting on top of box 1.
A massless rope passes over a massless, frictionless pulley. One end of the
rope is connected to box 2, and the other end is connected to box 3. The
weights of the three boxes are W1 = 55 N, W2 = 35 N, and W3 = 28 N. Determine
the magnitude of the normal force that the table exerts on box 1.
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 117
The three objects in the drawing are connected by strings that pass over
massless and friction-free pulleys. The objects move, and the coefficient of
kinetic friction between the middle object and the surface of the table is 0.100.
(a) What is the acceleration of the three objects? (b) Find the tension in each of
the two strings.