Chapter 4
The Laws of Motion
“If I have ever made any valuable discoveries, it has been
owing more to patient attention, than to any other talent.”
-Sir Isaac Newton
Classical Mechanics


Describes the relationship between the
motion of objects in our everyday world
and the forces acting on them
Conditions when Classical Mechanics
does not apply


very tiny objects (< atomic sizes)
objects moving near the speed of light
Forces



Force is a push or pull on an object
Force is Vector quantity
Force can be a contact force or a field force

Contact forces result from physical contact between two
objects

Field forces act between disconnected objects
 Also called “action at a distance”
 Examples of this force are
A.Contact force
I.
Pulling a spring
II.
Kicking a ball
III.
Pushing a wheelbar
B.Field force
I.
Elctric force i.e force of charge
II.
Gravitation force i.e force which cause an object to
move down
III.
Force of magnetic bar
Contact and Field Forces
Fundamental Forces


Types of Forces
 Strong nuclear force-between sub atomic
particles
 Electromagnetic force-between electric
charges
 Weak nuclear force -arises in certain
radioactive decay processes
 Gravity between objects
Classical physics, however, deals only with
gravitational and electromagnetic forces,
which have infinite range.
Units of Force

SI unit of force is a Newton (N)
kg m
1N  1 2
s
Newton’s First Law

An object at rest tends to stay at rest
and an object in motion tends to stay
in motion at a constant velocity unless
acted upon by an unbalanced force.


It takes force to change the motion of
an object.
The net force is defined as the vector
sum of all the external forces exerted
on the object
First Law Example

A soccer ball is sitting at rest. It takes
an unbalanced force of a kick to
change its motion.
External and Internal
Forces

External force


Any force that results from the
interaction between the object and its
environment
Internal forces


Forces that originate within the object
itself
They cannot change the object’s
velocity
Inertia


Is the tendency of an object to
continue in its original state of
motion
The First Law states that all objects
have inertia.
Mass




A measure of the resistance of an
object to changes in its motion due
to a force
The more mass an object has, the
more inertia it has (and the harder it
is to change its motion).
Scalar quantity
SI unit is kilogram (kg)
Newton’s Second Law

Acceleration of an object is direct proportion to its force and
inversely to its mass




A=
𝒎
𝒇
The net force of an object is equal to the product of its mass
and acceleration
 F = ma
 F and a are both vectors
When mass is in kilograms and acceleration is in m/s/s, the
unit of force is in newtons (N).
One newton is equal to the force required to accelerate one
kilogram of mass at one meter/second/second.
Second Law Cont.


F = ma basically means that the force of
an object comes from its mass (m) and its
acceleration (a).
Something very massive (high mass) that’s
changing speed very slowly (low
acceleration), like a glacier, can still have
great force.
Second Law Cont.

Something very small (low mass) that’s
changing speed very quickly (high
acceleration), like a bullet, can still have a
great force. Something very small
changing speed very slowly will have a
very weak force.
Sir Isaac Newton





1642 – 1727
Formulated basic
concepts and laws
of mechanics
Universal
Gravitation
Calculus
Light and optics
Gravitational Force


Mutual force of attraction between any two
objects in the universe.
Expressed by Newton’s Law of Universal
Gravitation:
m1 m2
Fg  G 2
r

where G = 6.67x10‒11 N. m2/kg2 is the
universal gravitation constant
Gravitational Force Cont.

Newton’s
law
of
universal
gravitation states that every particle
in the Universe attracts every other
particle with a force that is directly
proportional to the product of the
masses of the particles and inversely
proportional to the square of the
distance between them.
Weight

The magnitude of the gravitational
force acting on an object of mass
m near the Earth’s surface is
called the weight w of the object

w = mg is a special case of Newton’s
Second Law


g is the acceleration due to gravity
g can also be found from the Law
of Universal Gravitation
Weight Cont.
We know that
𝑤 = 𝑚𝑔
And
𝑀𝐸 𝑚
𝑤=𝐺 2
𝑟
Comparing the two equations, we get:
𝑀𝐸
𝑔=𝐺 2
𝑟
Where 𝑀𝐸 is the mass of the Earth.
More about weight

Weight is not an inherent property
of an object


mass is an inherent property
Weight depends upon location
Newton’s Third Law

For every action force acting on body
2 by body 1 there is an equal and
opposite reaction force acting on
body 1 by body 2.


F12  F21
Equivalent to saying a single isolated
force cannot exist
Newton’s Third Law cont.

F12 may be called the
action force and F21
the reaction force


Actually, either force
can be the action or
the reaction force
The action and
reaction forces act
on different objects
Third Law Example


The reaction of a rocket is an
application of the third law of
motion. Various fuels are
burned in the engine, producing
hot gases.
The hot gases push against the
inside tube of the rocket and
escape out the bottom of the
tube. As the gases move
downward, the rocket moves in
the opposite direction.
Action-Reaction Pairs

n and n '
n is the normal force,
the force the table
exerts on the TV
 n is always
perpendicular to the
surface
 n 'is the reaction – the
TV on the table
 n  n '

Action-Reaction pairs Cont.

Fg and Fg'
 F is the force the
g
Earth exerts on
the object
'
F
 g is the force the
object exerts on
the earth

Fg  Fg'
Forces Acting on an Object



Newton’s Law
uses the forces
acting on an
object
n and Fg are
acting on the
object
'
n ' and Fgare
acting on other
objects
Applications of Newton’s
Laws

Assumptions

Objects behave as particles



can ignore rotational motion (for now)
Masses of strings or ropes are
negligible
Interested only in the forces acting
on the object

can neglect reaction forces
Free Body Diagram



Must identify all the forces acting
on the object of interest
Choose an appropriate coordinate
system
If the free body diagram is
incorrect, the solution will likely be
incorrect
Free Body Diagram, Example

The force is the
tension acting on the
box


The tension is the same
at all points along the
rope
n and Fg are the
forces exerted by the
earth and the ground
Free Body Diagram, final

Only forces acting directly on the
object are included in the free
body diagram


Reaction forces act on other objects
and so are not included
The reaction forces do not directly
influence the object’s motion
Solving Newton’s
Second Law Problems


Read the problem at least once
Draw a picture of the system



Identify the object of primary interest
Indicate forces with arrows
Label each force

Use labels that bring to mind the
physical quantity involved
Solving Newton’s
Second Law Problems

Draw a free body diagram



Apply Newton’s Second Law


If additional objects are involved, draw
separate free body diagrams for each object
Choose a convenient coordinate system for
each object
The x- and y-components should be taken
from the vector equation and written
separately
Solve for the unknown(s)
Equilibrium


An object either at rest or moving
with a constant velocity is said to
be in equilibrium
The net force acting on the object
is zero (since the acceleration is
zero)
F  0
Equilibrium cont.

Easier to work with the equation in
terms of its components:
F
x

 0 and
F
y
0
This could be extended to three
dimensions
Equilibrium Example

A traffic light weighing 1.00x102 N
hangs from a vertical cable tied to
two other cables that are fastened
to a support, as in Figure 4.14a.
The upper cables make angles of
37.0° and 53.0° with the
horizontal. Find the tension in each
of the three cables.
Equilibrium Example –
Free Body Diagrams
Inclined Planes


Choose the
coordinate
system with x
along the incline
and y
perpendicular to
the incline
Replace the force
of gravity with its
components
Inclined Planes Example

A sled is tied to a tree on a frictionless,
snow-covered hill, as shown in Figure
4.15a. If the sled weighs 77.0 N, find
the magnitude of the tension force T :
exerted by the rope on the sled and
that of the normal force n: exerted by
the hill on the sled.
Multiple Objects




When you have more than one
object, the problem-solving
strategy is applied to each object
Draw free body diagrams for each
object
Apply Newton’s Laws to each
object
Solve the equations
Multiple Objects – cont.
Forces of Friction

When an object is in motion on a
surface or through a viscous
medium, there will be a resistance
to the motion



This is due to the interactions
between the object and its
environment
This resistance is called friction
That is resistance force of an
More About Friction





Friction is proportional to the normal force
The force of static friction is generally
greater than the force of kinetic friction
(Rolling, Sliding & Fluid friction)
The coefficient of friction (µ) depends on
the surfaces in contact
The direction of the frictional force is
opposite the direction of motion
The coefficients of friction are nearly
independent of the area of contact
Static Friction, ƒs





Static friction acts
to keep the object
from moving
If F increases, so
does ƒs
If F decreases, so
does ƒs
ƒs  µsn
At the verge of slipping ƒs
is maximum
Kinetic Friction,
ƒk


The force of
kinetic friction
acts when the
object is in
motion
ƒ k = µk n

Variations of the
coefficient with
speed will be
ignored
Block on a Ramp, Example



Axes are rotated as
usual on an incline
The direction of
impending motion
would be down the
plane
Friction acts up the
plane


Opposes the motion
Apply Newton’s Laws
and solve equations
Connected Objects




Apply Newton’s Laws
separately to each
object
The magnitude of the
acceleration of both
objects will be the
same
The tension is the
same in each diagram
Solve the simultaneous
equations
Connected Objects Cont.
More About Connected
Objects

Treating the system as one object
allows an alternative method or a
check

Use only external forces



Not the tension – it’s internal
The mass is the mass of the system
Doesn’t tell you anything about
any internal forces e.g Tension
force
Connected Objects –Problem1

A 5.00-kg object placed on a frictionless,
horizontal table is connected to a string that
passes over a pulley and then is fastened to a
hanging 9.00-kg object, as in the Figure below.
Draw free-body diagrams of both objects. Find
the acceleration of the two objects and the
tension in the string.
Connected Objects-Problem2

(a) A block with mass m1=4.00 kg and a ball
with mass m2 =7.00 kg are connected by a
light string that passes over a frictionless
pulley, as shown above. The coefficient of
kinetic friction between the block and the
surface is 0.300. Find the acceleration of the
two objects and the tension in the string.
(b) Check the answer for the acceleration by
using the system approach.