Transcript Force systems

Basic Biomechanics
BIOMECHANICS: BIO = living, MECHANICS =
forces & effects
 The application of mechanics to the living
organism involves the principles of anatomy and
physics in the descriptions and analysis of
movement
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Basic Biomechanics
 Mechanics-study of forces and motions produced by their
action.
 Biomechanics-apply that to the structure and function of
the human body.
Basic Biomechanics
 Anatomical Reference position: Erect standing position
with all body parts, including the palms of the hands,
facing forward; considered the starting position for body
segment movements
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Basic Biomechanics
 Anatomical Reference Planes: Cardinal planes – 3
imaginary perpendicular reference planes that divide
the body in half by mass
 Sagittal plane(rotates about frontal axis)
 Frontal plane(rotates about sagital axis)
 Transverse plane(rotates about longitudinal axis)
 Anatomical Reference Axis: Longitudinal axis, Frontal
Axis ,Sagittal Axis
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Force
 Force : Force is a mechanical disturbance which when
applied to a body may produce a chance in the existing
state of a body
 Thus a force when acting on a object ,can deform the
object, change its state of motion or both
 But a force will not always cause a change in motion
 E.g. if we sit on a chair then our wt is the force acting
on the chair, but the chair remains stationarystationary force
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Properties
 Force is a vector quantity
Thus in order to describe a force we need to know
1)pt of application
2)line of action of force
3)sense along which the force is acting
4)Magnitude
 Forces can be added graphically and trigonometrically
 Dimensions and units: F=ma ,unit-newton/kg-m/s^2
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Types Of forces
 There are some forces constantly present in nature
1) Gravitational Force: Every object on the surface of the
earth or near it, is attracted towards the center of
center of the earth
 F=mg
 Example: Gravitational force on a planet X is 40% of
that found on the earth. If the person weighs 667.5 N
on the earth, what is the persons weight on planet X?
 What is the persons mass on the earth and planet X?
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Types Of forces
 Gravitational force on earth = 9.81
 Gravitational force on planet X=0.4*9.81=3.92
 Mass of the person on earth, planet X= 667.5/9.81=68
 Weight of the person on planet X=68*3.92=266.72
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Types Of forces
2)Reaction : A force generated when an object applies a
force on another object in contact with it
3)Friction : When two bodies are in surface contact with
each other a force is generated as one of them starts
moving over the other. The force of friction is the one
which opposes the force causing movement of the
body on the surface of the other
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 4)Inertia : Inertia force is present in every object which
tends to resist any attempt to change its existing state
of rest or motion by application of force from outside
 Law of Acceleration-the amount of acceleration
depends on the strength of the force applied to an
object.
Types Of forces
 Forces can also be classified according to their effect on the bodies
upon which they are applied
1)External & Internal: External forces are commonly known forces like
while kicking a football, hammer a nail, a external force is applied on
the football, nail
2)Normal and Tangential forces: If a force is applied in a direction
perpendicular to the surface then it is called a normal force
A tangential force is that applied on the surface in the direction of the
surface.eg:Frictional force.
3)Tensile and compressive forces: Tensile force is the one which stretches
or elongates a body.eg:rubber band,muscles contract to produce tensile
force that pulls together the bones to which they are attached.
Compressive forces:These are the forces which shrink the body upon
which they are acting. Eg: Poking a needle into an inflated balloon.
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Resolution
 Resolution of a force implies breaking a force in the components
,such that the components combined together will have the same
effect as the original force
F
ѳ
F1
F
Fx
F
ѳ
ѳ
F2
Fy
 The force f acting at an angle theta can be resolved into two
forces F1 and F2.
 The components Fx and Fy are known as the perpendicular
components of force since they are perpendicular to each other
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Force Systems
 System of forces tells us the arrangement of forces and
is classified as follows:

system of forces
coplanar
concurrent
parallel
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noncoplanar
general
Coplanar force system
 In this arrangement all forces lie in one plane
y
f2
f1
f3
f4
x
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Coplanar force system
A
T1
T2
W
 A)Concurrent: In this system all the forces meet at a
point.
 E.g. A lamb hanging from two strings
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Coplanar force system
 two or more forces act from the same common point
but pull in different directions
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B)Parallel force system: In these forces line of action of
p3
forces are parallel
p2
p1
w
R1
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E.g. 3 people sitting on a bed
R1
coplanar force system
General system: Also known as a non concurrent &
non parallel system, has forces which do not meet at a
single point, nor are parallel to each other
F1
F3
F2
F4
Non coplanar force system
 When the forces acting on a system do not lie in a
single plane, they are termed as non coplanar forces or
space forces
y
f1
f3
z
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f2
x
Combination of forces
 Combination means to combine the forces acting in a
system into a single force which has same effect as the
no of forces acting together
 Such a force is known as the resultant of the system
 Finding the resultant helps us to understand the effect
of forces on the system and may form an important
step to solution of engineering problems
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Resultant of concurrent force system
 Parallelogram law of forces: If two forces acting
simultaneously on a body at a point are represented in magnitude and
direction by 2 adjacent sides of a parallelogram then their resultant is
represented in magnitude and direction by the diagonal of the
parallelogram which passes through the point of intersection of the
two sides representing the forces.
Mathematically R^2=(p^2+q^2+2pqcos ά) & tan θ= q sin ά
p+q cos ά
c
q
D
p
ά
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q
A
R
ά θ
p
B
Resultant of concurrent force system
 Example: Find the magnitude of the forces p & q such
that if they act at right angles their resultant is √34.If
they act at an angle of 60 their resultant is 7 N
 p2+ q2+2pqcos 90 =34
 p2+ q2=34………………………..(1)
 p2+ q2+2pqcos 60=49
 p2+ q2+pq=49,so pq=15,Thus p=15/q…………….(2)
 Put (2) in (1)
P= ,q=
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Resultant of concurrent force system
 Method of resolution:
1)Resolve the inclined forces if any in horizontal x direction and vertical y
direction
2)Add up the horizontal forces to get ∑Fx
3)Add up the vertical forces to get ∑Fy
The resultant force R=√(∑Fx^2+∑Fy^2)
Tan θ= ∑Fy/ ∑Fx
Example: Find the resultant of 4 concurrent forces acting on a particle P
500 N
300 N
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250 N
30
P
45
400 N
Resultant of parallel force system
 Since in a parallel system the forces are in one
direction they can be added up using a sign convention
for the sense of force
R=∑F
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Equilibrium Of forces
 A body is said to be in equilibrium if it is in the state of
rest or uniform motion.
 For the body to be in equilibrium the resultant of the
system should be zero. This implies:
1)The sum of all forces should be zero ∑F=0
2)The sum of all moments should be zero ∑M=0
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Equilibrium Of forces
 Eg: skier moving at constant speed down a slope:
Gravitational force
from Earth on skier
Frictional force
from Earth on skier
Contact force from
Earth on skier
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Equilibrium of a two force body
 If only two forces act on a member and the member is
in equilibrium then the 2 forces would be of equal
magnitude, opposite in direction and collinear
 Such members are referred to as 2 force members and
their identification is useful in solution of equilibrium
problems
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Equilibrium of a two force body
 A frame consist of three members Af,BC and DE
 Member BC is isolated
 Let Rb and Rc be the pin reactions at points B and c respectively
 Since only 2 forces are acting on a member BC it is a 2 force member
 Therefore Rb=Rc in magnitude, opposite in direction and collinear

F
Rb
B
B
B
D

C
A
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E
W
C
C
Rc
Equilibrium of a three force body
 IF three coplanar forces act on a member and the
member is in equilibrium then the forces would be
either concurrent or parallel
 Concurrent:
 Parallel:
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p
A
C
Ra
B
Rb
Equilibrium of concurrent forces
 Conditions of equilibrium for concurrent system of
forces in a plane:
 ∑Fx=0
 ∑Fy=0
 Or
∑Fx=0
∑Ma=0
 or
∑Ma=0
∑Mb=0
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Equilibrium of concurrent forces
 Triangle law of forces: When a set of 3 concurrent
forces are in equilibrium, they can be represented in
magnitude and direction with 3 sides of a triangle
Conversely when 3 concurrent forces can be
represented by the 3 sides of a triangle, they are in
equilibrium.
P
Q
P
Q
R
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R
Equilibrium of multiple coplanar forces
 Polygon Law of Forces: If a set of multiple coplanar
forces acting concurrently on a body are in equilibrium
then they can be represented in magnitude and
direction by the sides of a polygon having number of
sides equal to number of forces.
 Thus 5 forces can be represented by a pentagon and so
on.
q
p
r
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r
s
t
q
s
t
p
Equilibrium of parallel forces
 A force has a tendency to rotate a body about a point.
This tendency is known as its moment.
 Moment is a vector quantity. Magnitude of moment is
given by following expression: MA= F.d where F=mg,
d=perpendicular distance of the force from the
moment centre, MA= magnitude of moment about pt A
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Conditions for Equilibrium:∑F=0
∑Ma=0 where a is any pt on the plane but not on y-axis
 Or
 or
∑Ma=0 Where a and b are any 2pts on the plane but
line AB is not parallel to the forces
∑Mb=0
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Equilibrium of general force system
Conditions for Equilibrium of a general force system:
∑Fx=0
∑Fy=0
∑Ma=0 Where a is any pt on the plane but not on y-axis
 Or
∑F=0
∑Ma=0
∑Mb=0
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Lami’s Theorem
 If three concurrent forces are in equilibrium then the
magnitude of each force is proportional to the sine of
the angle between the other two forces in the system.
F1
F2
ѳ3
ѳ2
ѳ1
F3
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Lami’s Theorem
F1
=
F2
Sin(180-ѳ1)
Sin(180-ѳ2)
 F1
=
F2
Sin ѳ1
Sinѳ2
=
F2
ѳ1
ѳ2
F3
F1
ѳ3
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F3
Sin(180-ѳ3)
=
F3
Sin ѳ3
Equilibrium
 Stable Equilibrium: If a rigid body in the state of rest
is slightly disturbed from its initial position, return to
its initial position of equilibrium then it is said to be in
stable state of equilibrium
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Equilibrium
 Unstable Equilibrium: If a rigid body in the state of
rest is slightly disturbed from its initial position, does
not return to its initial position of equilibrium then it
is said to be in unstable state of equilibrium
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Equilibrium
 Neutral Equilibrium: If a rigid body in the state of
rest is slightly disturbed from its initial position,
remains in the state of rest at the new position then it
is said to be in neutral equilibrium
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