Chapter No 4 Turning effect of forces

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Chapter No 4
Turning effect of forces
Parallel forces: if a number of forces act on a body such that their points of action are
different but direction of forces is parallel to each other is called parallel forces.
Parallel forces are two types
1. Like parallel forces: Those parallel forces which have same direction are called
like parallel forces
2. Unlike parallel forces: Those parallel forces which have opposite direction are
called unlike parallel forces
Addition of forces: The process by which two or more forces are added is called
addition of forces.
The vector sum of the forces on a body is important because it determines the
direction and behavior of the force. The rules used for addition of forces are given
below



In case of like parallel forces, add magnitude of the forces
In case of unlike parallel forces, subtract magnitude of the forces
In case of non parallel forces, special method is used called heat to tail rule.
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Head to tail rule: The method of adding forces in such way that the head of the first is
joint with the tail of the second and the head of the second is joint with the tail of the
third and so on is called Head to tail rule. The resultant force is obtained by joining the
tail of first to head of last force.
Example. Let cyclist is moving toward north at force F1 and wind is blowing toward east
at force F2. The net force on a cyclist according to head to tail rule will be F
Resolution of force: The process which is used to split a single force into its
component is called resolution of force. The components of force which are
perpendicular (making 90 angle) to each other is called rectangular components of the
force.
Explanation: consider force F which is making angle with x-axis. When the force F
is resolved into its rectangular components it will give Fx and Fy
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Magnitude of horizontal and vertical components
Magnitude and direction of resultant force.
As
F2 = Fx2 + Fy2 by Pythagorean Theorem
Torque or moment of force:
Definition: The tendency of a force to produce rotation in a body about an
axis is called torque or momentum of force.
OR
The turning effect of force on a body is called torque
Mathematically Torque produced in a body is equal to the product of force
and moment arm.
Torque = force X moment arm
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Factors affecting torque:
Torque depends upon two factors:
1. Magnitude of force (F): Greater the magnitude of force greater will
be torque
2. Magnitude of moment arm (r) : The perpendicular distance between
the axis of rotation and the line of the action of force is called the
moment arm of the force. The longer the moment arm of the force
greater will be torque.
Unit of Torque: Torque is a vector quantity and unit is Newton metre or
Nm.
Example: When we rotate the door, torque is produced. Greater the
force and longer the moment arm greater will be turning effect of door.
Types of Torque: there are two types of torque
1. Anticlockwise torque: If a body rotates about its axis in anti
clockwise direction then it is called anticlockwise torque and taken as
positive.
2. Clockwise torque: If the body rotates in the clockwise direction
then it is called clockwise torque and taken as negative.
Principle of moment: According to this principle
‘When a body is in equilibrium, the sum of clockwise moments must be
equal to the sum of anticlockwise moments’
For example, when the SEASAW is balanced at a pivot then clockwise
torque is equal to the anticlock wise torque.
Centre of mass: The point in a body at which mass is equally distributed in
all direction is called centre of mass. It is denoted by c.m
The force applied at this point will only produce linear acceleration.
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Example. The centre of mass of uniform wooden rod is its centre (mid
point)
Couple: The two parallel forces which are equal in magnitude but opposite
in direction and do not act along the same line of action is called couple.
The couple produces the rotational motion. The resultant force of a couple
is zero
For example, we apply forces with our two hands to turn the steering wheel
of the vehicle as a couple. When both hands apply the forces which are
equal in magnitude but opposite in direction wheel rotates due to couple.
Statics
Static is the branch of mechanics which deals with the study of bodies at
rest under a number of forces. For example, the equilibrium, conditions of
equilibrium, types of equilibrium, torque etc.
Equilibrium
Definition: A body is said to be in equilibrium if it is at rest or moving with
uniform velocity. OR
If the linear and angular acceleration of a body are zero, the body is said to
be in equilibrium.
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Explanation: when two or more forces act on a body such that their
resultant or combining effect on the body is zero and the body retains its
state of rest or of uniform motion then the body is said to be in
equilibrium.
Example
A book lies on the table, suspended bodies, all stationary bodies , jump
by using parachute.
Types of equilibrium
With respect to the state of a body, equilibrium may be divided into two
categories:
1. Static equilibrium
If the combined effect of all the forces acting on a body is zero and the
body is in the state of rest then its equilibrium is termed as static
equilibrium.
For example: All stationary bodies
2. Dynamic equilibrium
When a body is in state of uniform motion and the resultant of all forces
acting upon it is zero then it is said to be in dynamic equilibrium.
For example: Jump by using parachute.
Conditions of equilibrium
There are two conditions of equilibrium given below.
First condition of equilibrium
Definition: A body will be in equilibrium if the sum of all the forces acting
on the body is zero
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Mathematically:
where F= Fx + Fy +Fz
Explanation: According to first condition of equilibrium, to maintain
transitional equilibrium in a body the sum of all the forces acting on the
body is equal to zero. In other words we can say that to maintain
equilibrium the sum of all the forces acting along X-axis is equal to the
sum of all forces acting along Y-axis.
For example, stationary person
Second condition of equilibrium
Definition: A body will be in equilibrium if the sum of all the torques acting
on the body is zero
Mathematically:
where = sum of clockwise torque + sum of anticlockwise torque
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Explanation: According to second condition of equilibrium a body will be
in rotational equilibrium when the vector sum of all the torques acting on it
is zero. When the sum of all torques on the body is zero there will be no
change in the rotational motion of the body and a body is said to be in
rotational equilibrium.
Stability: A body in equilibrium is called stability of the body. Stability of
the body depends upon the position of the centre of the gravity of the body.
There are three states of equilibrium on the basis of stability.
1. Stable equilibrium
When the center of gravity of a body lies below point of suspension or
support, the body is said to be in stable equilibrium.
For example a book lying on a table is in stable equilibrium. In stable
equilibrium the body will come back to its original position when slightly
disturbed.
Reason of stability
When the book is lifted its center of gravity is raised . The line of action of
weight passes through the base of the book. A torque due to weight of
the book brings it back to the original position.
2. Unstable equilibrium
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When the center of gravity of a body lies above the point of suspension or
support, the body is said to be in unstable equilibrium. In unstable
equilibrium the body will not come back to its original position when slightly
disturbed.
Example
pencil standing on its point or a stick in vertically standing position.
Reason of instability
when the pencil is slightly disturbed its center of gravity is lowered . The
line of action of its weight lies outside the base of pencil. The torque due to
weight of the pencil toppled it down.
3. Neutral equilibrium
When the center of gravity of a body lies at the point of suspension or
support, the body is said to be in neutral equilibrium. Example: rolling
ball.
Reason of neutral equilibrium
If the ball is rolled, its center of gravity is neither raised nor lowered. This
means that its center of gravity is at the same height as before.
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Exercise
Objectives
1. D 2. B 3. C 4. D 5. C 6. B 7. A 8. B 9. A 10. A
Conceptual questions.
1. In which of the following case or cases, there is no horizontal force on
the suitcase and why
In case (a),, there is no horizontal component because the force
acting on the suitcase is perpendicular. So when the force is resolved
into its component it will have only Fy components no Fx as original
force lie perpendicular.
2. In which case the x and y components are equal to one another.
Explain.
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In case B, the force
rce makes angle of 45 so horizontal and vertical
components must have same value.
Fx = FCos = 100 cos 45 = 100x 0.707 = 70.7N
Fy = FSin = 100 sin 45 = 100x 0.707 = 70.7N
3. Why is it more difficult to lean backwards? Explain
Reason: It is more difficult to lean backwards because the centre of
gravity of the body lower and unstable equilibrium establishes and
difficult to come back to original position.
4. Explain why door handles are not put near the hinges?
Reason: Door handles are not put near to hinges beca
because
use moment of arm
will be short and turning effects or torque directly depend upon moment of
arm. Therefore it will be too hard to open or rotate the door when handles
are put near the hinges. To minimize force door handles are not put near to
hinges.
5. Why a helicopter does have a second rotor on its tail?
Reason: The main rotors of the helicopter produce torque which could
disturb equilibrium of helicopter or cause the helicopter to rotate.
rotate In order to
keep the helicopter at equilibrium or in straight motion the sum of all
torques must be zero. Therefore a second rotor is installed on helicopter
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tail to cancel the effect of main rotor or to balance clockwise rotation to
anticlock wise rotation.
6. Why is it better to use a long spanner rather a short one to tight
ti
a nut
on a bolt?
Reason. We know the equation of torque
From above equation it is clear that it is better to use a long spanner
rather a short one to tight a nut on a bolt because moment of arm
increases which increase torques and reduce the required force.
7. Which of these glasses in the most stable explain.
From figure, the glass C is more stable because if we disturb their
equilibrium by applying small force the glass c will easily come back to
its original position as compared to glasses A and B.
8. A girl is seated safely and steadily in a canoe when she tries to stand
up the canoe capsizes explain.
Reason: A girl is seated safely and steadily in a canoe because the
centre of mass is uniformly distribute so centre of gravity in this case
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cannot be changed easily but when she tries to stand up the centre of
gravity changes and unstable equilibrium establishes due to which hard
to keep in standing position.
9. How you determine the centre of irregular shape body?
Reason: to find the centre of mass of irregular shaped body, make three
holes at different position. Suspend the body from theses holes and
draw lines. The intersection of these lines gives centre of gravity of
irregular shaped body.
10.
The gravitational force acting on a satellite is always directed
towards the centre of the earth. Does this force exert torques on
satellite?
Reason. The gravitational force acting on a satellite is always directed
towards the centre of the earth but it does not exert torque on satellite
because for central force r is zero and hence the torque is zero. In this
case force is applied on axis of rotation (centre of earth). Additionally as
torque = rxf= rfsin where = 180 so torque = 0 because sin180= 0.
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