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Newton’s Laws and Gravity
Mass, Weight, Force, Friction.
Application of Newton’s Laws
o Introduce Newton’s three laws of motion
 At the heart of classical mechanics
 Describe a vast range of physical phenomena
 Example: Newton’s laws explain the motion of stars and planets.
o Frictional force between objects.
 Static and kinetic friction,
 Coefficients for static and kinetic friction.
Lecture 4
o Aim of the lecture
 Concepts in Mechanics
 mass weight and force
 Frictional Forces
 Newton’s Laws
o Main learning outcomes
 familiarity with
 mass, weight
 static and moving friction, coefficients
 Newton’s First Law
 Newton’s Second Law
 Newton’s Third Law
 ability to
 use Newton’s Laws in linear problems
 use coefficients of friction
Newton’s First Law
o It appears that:
 A force is needed to keep an object moving at constant speed.
 An object is in its “natural state” when at rest.
o These are wrong
 friction creates this illusion.
o Example:
 An object sliding with an initial speed vo will stop:
 Quickly on a rubber sheet
 Slowly on ice
 Never if there is no friction.
o Newton was first to recognize this.
 Checked using the motion of the moon and the planets.
 In space there is no friction, he was able to derive
 “Newton’s first law”
If there is no force acting on a body, its velocity
cannot change; that is the body cannot accelerate
Newton’s First Law
o The meaning of force is defined by Newton.
o Before Newton the word force was not even used:
o bodies had ‘influence’ on them
o A body in a state of constant motion has no force on it.
y
x
Note: If several forces act on a body (say FA , FB , and FC ) the net force Fnet
is defined as: Fnet  FA  FB  FC i.e. Fnet is the vector sum of FA , FB , and FC
o What is mass?
o characteristic that relates a force F applied on the body and the resulting
acceleration a.
o Then what is the relation between a force applied on the body and the resulting
acceleration ?
o The answer is the Newton’s Second Law!
Newton’s Second Law
Fnet
m
a
The net force on a body is equal to the product
of the body’s mass and its acceleration
Fnet  ma
The above equation is a compact way of summarizing three separate equations,
one for each coordinate axis:
Fnet , x  max
Fnet , y  ma y
Fnet , z  maz
o What is the difference between the mass and the weight ?
o In order to answer this question we need to know the concept of gravitational force.
The Gravitational Force: It is the force that the earth exerts on any object (in the
picture a cantaloupe) It is directed towards the center of the earth. Its magnitude
is given by Newton’s second law.
Fg  ma  mgjˆ
Fg  mg
o Now we are in a position to answer the above question.
Weight: The weight of a body is defined as the magnitude of the force
required to prevent the body from falling freely.
g
W
y
mg
Fnet , y  ma y  W  mg  0  W  mg
So the weight of an object is not its mass. If the object is moved to a location where
the acceleration of gravity is different (e.g. the moon where gm = 1.7 m/s2) , the mass
does not change but the weight does.
o Except the mass and the weight what else do we know before applying Newton’s Laws
to a system ?
o The answer is: Friction, normal force, and the tension.
FN
Normal Force: When a body presses against a surface, the
surface deforms and pushes on the body with a normal force
perpendicular to the contact surface. An example is shown in
the picture to the left. A block of mass m rests on a table.
Fg
Note: In this case FN = mg. This is not always the case.
Direction of attempted
slide
Direction of friction force: f
Friction: If we slide or attempt to slide an object over
a surface, the motion is resisted by a bonding
between the object and the surface. This force is
known as “friction”.
Tension: This is the force exerted by a rope or a cable attached to an object Tension
has the following characteristics:
1. It is always directed along the rope
2. It is always pulling the object
3. It has the same value along the rope.
The following assumptions are made:
a.The rope has negligible mass compared to the mass of the object it pulls
b.The rope does not stretch.
If a pulley is used we assume that the pulley is massless and frictionless.
T
T
The rope is pulling by a
force F
T
T
The rope is pulling by a
force F
Newton’s Third Law:
Book B
FBC
Crate C
When two bodies interact by exerting forces on
each other, the forces are equal in magnitude
and opposite in direction
FCB
For example consider a book leaning against a bookcase. We
label FBC the force exerted on the book by the case. Using the
same convention we label FCB the force exerted on the case by
the book. Newton’s third law can be written as : FBC = -FCB .
A second example is shown in the picture. The third-law
pair consists of the earth and a cantaloupe. Using the same
convention as above we can express Newton’s third las as:
FCE = - FEC .
Applying Newton’s Laws / Free body Diagrams
Part of the procedure of solving a mechanics problem using Newton’s laws is drawing
a free body diagram. This means that among the many parts of a given problem we
choose one which we call the “system”. Then we choose axes and enter all the
forces that are acting on the system and omitting those acting on objects that were not
included in the system.
Recipe for the application of
Newton’s law’s of motion
1. Choose the system to be studied
2. Make a simple sketch of the system
3. Choose a convenient coordinate system
4. Identify all the forces that act on the system. Label them on
the diagram
5. Apply Newton’s laws of motion to the system