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STATICS OF PARTICLES

FORCE:

Force is an external agency which is applied on the body to change the state of rest or state of uniform motion unit: Newton

SYSTEM OF FORCES:

FORCE

CO-PLANAR FORCE NON-COPLANAR FORCE

CONCURRENT CONCURRENT

NON CONCURRENT NON CONCURRENT

LIKE COLLINEAR PARALLEL

UN LIKE COLLINEAR NON PARALLEL

NON PARALLEL

PARALLEL

RESULTANT OF A FORCE:

The resultant of a force system is a single force which produces the same effect as that of the force system. It is an equivalent force of all the given forces.

PARALLELOGRAM LAW OF FORCES:

If two forces acting at appoint can be represented in magnitude and direction by the two adjacent sides of a parallelogram their resultant can be represented magnitude and direction by the diagonal of the parallelogram passing through the point.

R=root of (p2+q2+2pqcosØ)

tanØ=qsinØ/p+qcosØ

Where p and q are forces

TRIANGLE LAW OF FORCES:

If two forces acting on a body are represented by the sides of a triangle then the resultant is represented by the third side of the triangle taken in the opposite order

The two forces P&Q are acting on O .The line OA and OB represents the forces P and Q respectively the resultant of P&Q in magnitude line of action and direction.

This method is applicable to determine the resultant of system consisting only two forces.

POLYGON LAW OF FORCES:

If any number of forces are represented in magnitude and direction by the sides of polygon taken in order their resultant is represented by closing side of the polygon taken in opposite order.

This method is used when we have number of forces.

 

EQULIBRIUM OF A PARTICLE:

A particle is said to be in equilibrium when the resultant of all the forces acting on it is zero.

In graphical terms; the particle is in equilibrium when the force polygon closes.

In other terms, a body is said to be in equilibrium when it comes back to its original position after it is slightly displaced from its position of rest.

RESULTANT OF SEVEREL FORCES ACTING ON A PARTICLE:

If several forces act on a particle, then the resultant force (F) is obtained by adding the algebraic sum of horizontal (Fx) and vertical (Fy) components of the individual forces, taking into consideration the direction of forces.

Most problems in mechanics deal with system of forces and it is usually essential to reduce the system to a single force called the resultant force. The resultant of system of forces is a combination of original individual forces which will have same external effect on the body upon which the forces act. The resultant (F) of the system of coplanar concurrent forces.

R=F1+F2+F3+……………=SF

Rx=SFx Ry=SFy

R=root of ((SFx)2+(SFy)2)

Ø=tan-1(Ry/Rx)= tan-1(SFy)/(SFx)

Where R is the resultant force,

SFx(or)Rx is the algebraic sum of the x components

SFy(or)Ry is the algebraic sum of the y components

and Ø is the direction of the resultant force.

RESOLUTION OF FORCE INTO RECTANGULAR COMPONENTS:

The resultant force F is resolved into its components Fx &Fy where Ø is the angle of the resultant force with respect to the X-axis the magnitude of the components are

Fx =Fcos Ø and Fy =FsinØ

F=root of (Fx2+Fy2), Ø=tan-1(Fy/Fx)

If more than one force is acting in a system, then Fx is the algebraic sum of the components of forces along the x-axis and Fy is the algebraic sum of the components of forces along the y-axis and the positive x-axis positive y-axis are taken as positive and forces acting along the negative X and negative Y-axis are taken as negative.