Basic Biomechanics BIOMECHANICS BIO living MECHANICS forces effects

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 Chaitali Prabhudesai

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 Chaitali prabhudesai

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 Chaitali Prabhudesai

Chaitali Prabhudesai

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 stationary force Chaitali Prabhudesai

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 Chaitali Prabhudesai

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 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? Chaitali Prabhudesai

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 Chaitali prabhudesai

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 Chaitali Prabhudesai

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. Chaitali Prabhudesai

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 F 1 F Fx F ѳ ѳ F 2 Fy The force f acting at an angle theta can be resolved into two forces F 1 and F 2. The components Fx and Fy are known as the perpendicular components of force since they are perpendicular to each other Chaitali Prabhudesai

Force Systems System of forces tells us the arrangement of forces and is classified as follows: system of forces coplanar concurrent parallel Chaitali Prabhudesai noncoplanar general

Coplanar force system In this arrangement all forces lie in one plane y f 2 f 1 f 3 f 4 x Chaitali Prabhudesai

Coplanar force system A T 1 T 2 W A)Concurrent: In this system all the forces meet at a point. E. g. A lamb hanging from two strings Chaitali Prabhudesai

Coplanar force system two or more forces act from the same common point but pull in different directions Chaitali prabhudesai

B)Parallel force system: In these forces line of action of p 3 forces are parallel p 2 p 1 w R 1 Chaitali Prabhudesai E. g. 3 people sitting on a bed R 1

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 F 1 F 3 F 2 F 4

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 f 1 f 3 z Chaitali Prabhudesai f 2 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 Chaitali Prabhudesai

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+2 pqcos ά) & tan θ= q sin ά c q D p ά Chaitali Prabhudesai q A R ά θ p B p+q cos ά

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 p 2+ q 2+2 pqcos 90 =34 p 2+ q 2=34……………. . (1) p 2+ q 2+2 pqcos 60=49 p 2+ q 2+pq=49, so pq=15, Thus p=15/q……………. (2) Put (2) in (1) P= , q= Chaitali Prabhudesai

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 Chaitali Prabhudesai 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 Chaitali Prabhudesai

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 Chaitali Prabhudesai

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 Chaitali prabhudesai

Chaitali prabhudesai

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 Chaitali Prabhudesai

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 Chaitali Prabhudesai 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: Chaitali Prabhudesai 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 Chaitali Prabhudesai ∑Mb=0

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 R Chaitali Prabhudesai 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 Chaitali Prabhudesai 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 Chaitali Prabhudesai

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 2 pts on the plane but line AB is not parallel to the forces ∑Mb=0 Chaitali prabhudesai

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 yaxis Or ∑F=0 ∑Ma=0 ∑Mb=0 Chaitali Prabhudesai

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. F 1 F 2 ѳ 3 ѳ 2 ѳ 1 F 3 Chaitali Prabhudesai

Lami’s Theorem F 1 = F 2 Sin(180 -ѳ 1) Sin(180 -ѳ 2) F 1 = F 2 Sin ѳ 1 Sinѳ 2 = F 2 ѳ 1 ѳ 2 F 3 F 1 ѳ 3 Chaitali Prabhudesai F 3 Sin(180 -ѳ 3) = F 3 Sin ѳ 3

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 Chaitali prabhudesai

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 Chaitali prabhudesai

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 Chaitali prabhudesai