CHAPTER
1 FORCE
Kinds of Forces
• Force
is a physical cause which changes (or tends to change) either the size or shape
or the state of rest or motion of the body.
• The
forces which act on bodies when they are in physical contact are called contact
forces.
• When a
body moves over a rough surface, a force acts on the body in a direction
opposite to the motion of the body along the surface of contact. This is
called the frictional force or the force of friction.
• When a
person moves towards the right on a road, the force of friction acts on him
towards the left. This force resists his motion on the road.
• When a
body is placed on a surface, the body exerts a force equal to its weight in the
downward direction on the surface. However, the body does not move (or
fall) because the surface exerts an equal and opposite force on it, which
is called the normal reaction force.
• When a
body is suspended by a string, the body pulls the string vertically downwards
due to its weight. In its stretched condition, the string pulls the body
upwards by a force which balances the weight of the body. This force
developed in the string is called the tension force T.
• The
spring has a tendency to return to its original form. Similarly, when one end
of a spring is kept fixed, the spring is found to exert a force at its
other end which is directly proportional to the displacement, and the
force exerted is in a direction opposite to the direction of displacement.
This force is called the restoring force.
• When
two bodies collide, they push each other. As a result, equal and opposite
forces act on each body.
• The
forces experienced by bodies even without being physically touched are called
non-contact forces or forces at a distance.
• In the
Universe, each particle attracts another particle because of its mass. This
force of attraction between the particles is called the gravitational
force.
• The
force on a body due to the Earth’s attraction is called the force of gravity.
It causes the movement of the body towards the Earth, i.e. downwards, if
the body is free to move. The body also attracts the Earth by an equal
amount of force, but no motion is caused in the Earth because of its huge mass.
• Two
like charges repel, while two unlike charges attract each other. The force
between the charges is called the electrostatic force.
• Two
like magnetic poles repel each other, while two unlike magnetic poles attract
each other. The force between the magnetic poles is called the magnetic
force.
General Character of Non-contact Forces
1. The
gravitational force is always of an attractive nature, while the electrostatic
force and the magnetic force can be either attractive or repulsive.
2. The magnitude of
non-contact forces on the two bodies varies inversely as the square of
the distance of separation between them. It decreases with an increase in
separation and increases as the separation decreases.
Newton’s First Law of motion
• Newton’s
First Law: A body remains in the state of rest or of uniform motion in a
straight line unless an external force is applied on it.
• The
property of an object by virtue of which it neither changes its state nor tends
to change its state is called inertia. It is an inherent property of each
object.
Newton’s Second Law of Motion
• Newton’s
Second Law: The rate of change of momentum of a body is directly proportional
to the applied force and takes place in the direction in which the force acts.
Momentum
• The
force required to stop a moving body is directly proportional to the mass and
velocity of the body.
• The
momentum ‘p’ of a body is defined as the product of mass ‘m’ and velocity ‘v’
of the body. p = mv
• If a
body is at rest, then its momentum will be zero.
• Momentum
has both magnitude as well as direction; hence, it is a vector quantity.
• The SI unit of momentum is kg.m/s
• Thus,
the rate of change of momentum is the product of mass and acceleration.
• From
Newton’s law, F ∝ ma or F = kma
• In SI
units, k = 1 F = ma
• In the
vector form, the above equation is written as
• The
acceleration produced in a body of a given mass is directly proportional to the
force applied on it. a ∝ F
• The
acceleration produced in a body is inversely proportional to the mass of the
body. a ∝ 1 / m
Newton’s Third Law of Motion
• Newton’s
Third Law: To every action, there is an equal and opposite reaction.
• When
you pull a spring with both hands, you feel an equal force trying to pull the
spring back.
• Thus,
in an interaction of two bodies, there are action and reaction forces present.
However, we should note that the action and reaction forces act on two
different bodies.
• In the
CGS system, the unit of force is dyne.
1 dyne = 1 g × 1 cm s−2
• SI
unit: The SI unit of force is newton (N).
1 N = 1 kg × 1 m s−2
• One
newton (N) is that force which when acting on a body of mass 1 kg produces an
acceleration of 1 m s−2 in it.
• 1 N =
105 dyne
• The gravitational
unit of force in the MKS system is kilogram force (kgf).
1 kgf = 1 kg × 9.8 m s−2
1 kgf = 9.8 N
• One
kilogram force is the force with which the Earth pulls a body of mass 1 kg
towards itself.
• The
three equations of motion considered for a body moving with uniform
acceleration are
1) v = u + at
2). s = ut + 1 / 2 at2
3). v2 = u2 + 2as
Here, ‘u’ is the
initial velocity, ‘v’ is the final velocity, ‘a’ is the acceleration and ‘s’ is
the distance.
Translational and Rotational Motion
• When a force
acts on a stationary rigid body which is free to move, the body starts moving
in a straight path in the direction of the force. This is called linear or
translational motion.
• When
the body is pivoted at a point, the force applied on the body at a suitable
point rotates
Moment of a Force or Torque
• The
turning effect of the force acting on the body about an axis is due to the
moment of force or torque.
• The
factors affecting the turning of a body are
I. Magnitude of the
force applied
II. Distance of the
line of action of the force from the axis of rotation
• The
moment of force (or torque) is equal to the product of the magnitude of the
force and the perpendicular distance of the line of action of force from
the axis of rotation.
Clockwise and Anticlockwise Moments
• The
direction of turning (or sense of rotation) produced on the body depends on the
point of application of the force and on the direction of the force.
• Conventionally,
when the turning effect on the body is anticlockwise, the moment of force is
called the anticlockwise moment and it is taken as positive, while if the
turning effect on the body is clockwise, the moment of force is called the
clockwise moment and it is taken as negative.
• The
SI unit of the moment of force is newton metre (N m).
• In
gravitational units, the MKS unit is (kgf m) and the CGS unit is (gf m).
• 1
N m = 107 dyne cm
• 1
kgf m = 9.8 N m
• 1
gf m = 980 dyne cm
• For
turning a steering wheel, a force is applied tangentially on the rim of the
wheel. The sense of rotation of the wheel is changed by changing the point
of application of force without changing the direction of force.
• The
turning of a body about an axis depends not only on the magnitude of the force
but also on the perpendicular distance of the line of action of the
applied force from the axis of rotation.
• A
single force applied on a pivoted body alone does not cause turning or rotation
of the body.
• The
turning is always produced by a pair of forces.
• Such a
pair of forces is called a couple. Thus, two equal and opposite parallel forces
not acting along the same line form a couple. A couple is always needed to
produce rotation.
• For
example, when we open a door, the rotation of the door is produced by a couple
consisting of two forces: (1) the force which we exert at the handle of
the door, and (2) an equal and opposite force of reaction at the hinge.
Action of a Couple
• The
perpendicular distance between the two forces is called the couple arm.
• The two
forces cannot produce translational motion as their resultant sum is zero.
However, each force has the turning effect on the bar in the same
direction, so the two forces together form a couple which rotates the bar
about the point O.
Equilibrium of Bodies
• When
several forces acting on a body produce no change in its state of rest or of
motion, the body is said to be in equilibrium.
• When a
body remains in the state of rest under the influence of the applied forces,
the body is in static equilibrium.
• When a
body remains in the same state of motion under the influence of the applied
forces, the body is said to be in dynamic equilibrium.
Conditions for Equilibrium
1. The resultant of
all the forces acting on the body should be equal to zero.
2. The resultant
moment of all the forces acting on the body about the point of
rotation should be zero, i.e. the sum of the anticlockwise moments about
the axis of rotation must be equal to the sum of the clockwise moments
about the same axis.
Principle of Moments
• If the
algebraic sum of moments of all the forces acting on the body about the axis of
rotation is zero, then the body is in equilibrium. This is called the
principle of moments.
Sum of
anticlockwise moments = Sum of clockwise moments
Centre of Gravity
• The
force with which the Earth attracts every particle towards its centre is known
as the force of ravity. It is also known as the weight of the particle.
• A body
can be made up of several particles, each of weight ‘w’. As the size of the
body is quite small in comparison to the size of the Earth, the pull of
gravity w acting on these particles can be regarded as parallel to each
other.
• The magnitude of a single force is equal to the sum of all these parallel forces.
• Weight
W is considered to act at a point G such that the algebraic sum of moments due
to weight w of each particle about the point G is zero. The point G is called
the centre of gravity of the body.
• Centre
of gravity (CG) of a body is the point about which the algebraic sum of moments
of weights of all the particles constituting the body is zero. The entire
weight of the body can be considered to act at this point.
• It is
not necessary that the centre of gravity always lies within the material of the
body.
Centre of Gravity and balance point
• When a body is freely
suspended from a point, it comes to rest (or in balance) in such a position
that its centre of gravity lies vertically below the point of suspension.
• It is possible because the algebraic
sum of moments of the weights of all the particles about the point of
suspension is zero.
Uniform Circular Motion
• When an
object moves in a circle, its motion is called circular motion.
• When an
object moves along a circular path, its direction of motion as well as speed
changes continuously.
• Thus,
the motion is said to be accelerated motion because the speed (or velocity)
keeps changing.
• When
the body moves in a circle with uniform speed, its motion is known as uniform
circular motion.
Centripetal and Centrifugal Force
• The
force needed to make an object travel in a circular path is known as
centripetal force.
• This
force is always directed towards the centre of the circle at each point of its
path. Hence, for a body moving uniformly in a circular path, there must be
a force to provide the centripetal force required for circular motion.
• In an
atom, an electron moves around the nucleus in a circular path for which
the centripetal force is obtained from the electrostatic force of
attraction on the electron by the nucleus.
• A
planet moves around the Sun in a nearly circular path for which the
gravitational force of attraction on the planet by the Sun provides the
necessary centripetal force.
• The
force acting on a body away from the centre of the circular path is called the
centrifugal force.
• It is
not a real force. However, it is considered to describe a certain motion and is
called fictitious force or virtual force.
• Its
magnitude is the same as centripetal force. It is however not a reaction force
of centripetal force, because both the forces act on the same body
performing circular motion.
• A
bucket filled with water is swirled around. The water does not spill out of it
because of the centrifugal force acting on it away from the centre.
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