Mechanics is a branch of physics
which deals with the study of motion. There are different parts in mechanics like kinematics, dynamics and
statics. In kinematics we study the motion of the body alone without bothering
about the forces that are causing the motion. In dynamics we study not only the
motion of the body but also study the cause of the motion. In kinematics how is the only question that we always
rise whereas in dynamics we rise the question not only how but also why. Statics is a branch of mechanics which deals with
the bodies in the state of equilibrium.
While studying mechanics we
assume that the bodies are point sized and if they are not point sized we
imagine a point where the entire mass of the body is concentrated and that
particular point could be called as Centre of mass. Any body cannot change its state
itself and we need to make it change its position. To change the position of
the body will need to apply the force. Hence forces a physical quantity which
changes are at least tries to change the state of the body. To know how the bodies
change their state of motion or rest, we need to learn rules called the Newton
laws of motion. There are popularly three different Newton laws of motion.
Law of Inertia
The first Newton law of motion is
also called as law of inertia. Every body always tries to continue its state of
rest or state of motion unless some external force tries to change it. This
property is called inertia. If the body is in the state of rest it prefers to
continue in the state of rest itself unless some external force is applied on
it. This is called inertia of rest. Observing inertia of rest practically is
quite easy. Let us imagine you yourself in a bus in a standing position and the
bus is in the state of rest. If the bus starts all of a sudden, you feel a jerk
in the body. It is because your body is in the state of rest with respect to
the bus. When the bus starts the lower part of the body also starts because it
is directly in contact with the floor of the bus. But the upper part of the
body who is in the state of rest prefer to be in the state of rest because of
inertia of rest. Hence you feel like falling in the back ward direction.
Similarly if a body in the state
of motion, it prefers to be in the state of motion itself and it don’t like to stop. This property is called
inertia of motion. Understanding this is also very simple using the same
example that we have discussed in the above case. Let us consider you in a bus
in the standing position and a bus is in the state of motion. If the bus stops
all of a sudden, you feel like falling in the forward direction. It is just
because the lower part of the body starts with the bus as it is directly in
contact with the bus floor. But a part of the body that is in the state of
motion prefers to be in the state of motion and hence you feel like falling in
the forward direction. This is due to inertia of motion.
If a body is moving in a
particular direction it prefers to move in the same direction and it don’t like
to change the direction. This is called inertia of direction. We can use the same
example like a passenger standing in a bus. When the bus takes a turn, the
passenger feels like falling in the other direction of the turn just because of
inertia of direction. When the bus takes a turn, your body is supposed to take
the turn with the bus but because of the inertia of the direction it prefers to
move in the same earlier direction and hence you feel like thrown in the
opposite direction of the turn taken by the bus.
Altogether inertia is the
property of a body because of which the body tries to continue in its own state
unless some external forces is applied on it. This property could be called
like Newton’s first law of motion or Newton law of inertia.
Newton’s second law of motion
Newton’s second law of motion is
also called as law of force. Force is a physical quantity which change the position of
the body are at least tries to change the position of the body. According to
Newton’s second law of motion force can be defined as the rate of change of
momentum. Momentum is a physical quantity which is defined as a product of mass
and velocity. It is a vector quantity which has both magnitude and directions
and satisfies the rules of vectors. Depending on whether the mass of the bodies
constant are velocity of the body is constant, we can write the second Newton
laws of motion into different formats as shown below.
Force is measured with SI unit
called Newton and in CGS system it is measured with the unit called a Dyne.
Problem
Three forces are acting on a body
and the bodies in the equilibrium position. If one of the forces removed what
is the acceleration acquired by the body?
Solution:
When three forces acting
simultaneously the body is an equilibrium position which means the resultant of
the three forces is equal to 0. When
one forces removed equilibrium is lost and hence it is going to have a
resultant force in the effect to direction of the remaining two forces. The
resultant of the two forces can be obtained using the parallelogram law of the
vectors.
Problem:
A body of mass 1 kg is moving
with the velocity 30 meter per second due north. A force of 10 Newton is
applied along East for four seconds on the body. What is the velocity of the
body after the force stops acting.
Solution:
Initially the body is having
velocity only along the Y direction. There is no force acting along the Y
direction and hence velocity along the Y direction remains constant even after
the four seconds. Initially the body is not having any velocity along the X
direction but there is a force acting along the direction. And hence the body
will get and acceleration along the X direction. It also requires a velocity
along X direction during this four seconds and we can calculate the velocity
using the equation of motion. Now the body is having velocity both along X and
Y directions and hence we can calculate the effect to velocity in the format of
a vector and we can calculate its magnitude using the rules of the vectors as
shown below.
Newton’s third law of motion
The statement of this rule is
very simple and popular. For every
action, there is equal and opposite reaction. If we put a book on the
table, book applies a force on the table equal to its weight. It is action. The
table also reacts by applying the same force on the book in the opposite
direction. This is reaction. There is one simple thing that we need to
understand. Action and reaction are the two forces of equal magnitude but
opposite in the direction. Even then they don’t cancel each other, because they
are not acting on the same body rather than acting on the different bodies.
It
is clear and it is critical to understand that action and reaction doesn’t
cancel each other because they are not acting on the same body. If the reaction
is happening normal to the surface of the contact, then it can also be called as
normal reaction.
Apparent weight of a man in a
lift
Apparent weight is the weight
experienced by the man. It is actually the magnitude of the normal reaction
experienced by the man. The body applies the weight of the floor as an action
under normal circumstances, the floor applies the same reaction on the body
in the opposite direction with equal magnitude. If this force is perpendicular
to the surface of contact of the body, the reaction is called normal reaction.
When a man is in a lift who is
moving up or down with a constant velocity, the acceleration experienced by the
man is equal to acceleration due to gravity and hence the apparent weight is
equal to the normal weight itself.
If the man is in a lift to who is
moving up with a certain acceleration, he experience a apparent acceleration
that is more than acceleration due to gravity. The total normal reaction
experienced by the man is equal to the sum of the reaction applied by the earth
due to his weight as well as the force with which the lift is moving in the upward
direction. Because of this the apparent weight in this case appears like more
than that of the real weight.
If the lift is coming down with
and acceleration, then the normal reaction experienced by the man is equal to
the difference between the weight of the man as well as the force on the man
due to the up Ward directional acceleration of the lift. Does the apparent
weight appears like less than that of the real weight in this case. If the lift
is falling freely, then the weight is being cancelled by the upward force
applied by the lift and hence we feel like weightless.
We can write equations for the
apparent waiting different cases as shown below.
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