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Statics and Dynamics

Statics refer to the study of mechanics that deals with bodies at rest and forces like torque, moment in equilibrium .Relation of forces that produce equilibrium among material body  that do not have an acceleration.

As per Newton's law to system which states that F=MA , where F = total force, M= mass, A= acceleration measures a vector that has magnitude and direction. Sum of the force will give direction and magnitude of acceleration and it will be inversely related to mass. The assumption of static equilibrium leads to moments. Statics is mechanics with the idealization that the acceleration of mass is negligible in Newton's laws.

-It is a quantity that has static magnitude whereas vector has magnitude and direction. Vectors are calculated using different laws. Vectors are represented by orthogonal bases like I, j, k along x,y,z axes.

-Force - It is the push or pull. It tends to move a body in the direction of action. It has features like magnitude, direction and hence it is a vector quantity. It is classified as contact (means physical contact example force exerted on a body by a table) or body forces (it is the weight of body in the earth's gravitational field).

Statics is used in the study of structures for example in architectural and structural engineering. Strength of material is a field that depends on the application of static equilibrium. Center of gravity concept means body at rest; it represents an imaginary point where mass of a body resides. In response to external forces the position of point from the base on which the body depends determine stability.

Body is said to be unstable when center of gravity exists outside the base because there exists a torque which means any small disturbances will cause the body to fall and vice versa. If the center of gravity coincides with the base then it is said to have metastable.

Dynamics - It is the study of mathematic concerned with study of forces and torques and their effect on motion as opposed to kinematics and kinetic which study the motion of object. Kinematics is the study to relate displacement, velocity, acceleration and time without reference to the cause of motion. It is relating to the forces acting on the body. Kinetics is further divided into forward dynamics to predict the motion in relation to the forces acting on body and inverse dynamic to determine the forces to produce a given motion of a body. It is concerned with the motion of body under the action of forces which stimulate growth development or change within a system or process.

Equilibrium can be defined as any object when all forces acting upon it result in zero change of motion for the object. Static equilibrium indicates that the object is motionless. Dynamic equilibrium indicates that the object is moving, and will continue to unchanged.

In static equilibrium system, equilibrium will return to its original position when an outside force pushes a system out of equilibrium. Whereas dynamic equilibrium is a situation where an object  in equilibrium will not return to equilibrium once moved out of equilibrium. For example - if we place a stone  inside the glass at the point, at the vertically flat point on the edges of glass  it will return to the equilibrium point on its own when you push it away. If we put a stone outside the glass at the equilibrium point, at vertically on the edges of glass, it will not return to equilibrium point on its own when we push instead it will fall.

Dynamic takes into account for time dependent changes in the system while a static (steady state) model calculates the system in equilibrium and thus is time invariant. Dynamic models are represented by differential equations or difference quotients.

The target is to find equations of objects of motion in the system of rigid object that may roller slide or be in free bus. Multi-object system is also considered so long as they do not involve other kinematic constraints between the bodies. For example the steering dynamics of a car assume the car as a rigid object, whereas for crash analysis where rigidity is a poor approximation a car is highly deformable.

Sometimes solid parts are assembled to cause force or torque in one place hen a different force or torque is applied at another place. Such assemblies include levers, gear boxes, presses, pliers, clippers, chain drives, and crank-drives. Besides solid parts connected by pins, a few special purpose parts are commonly used, including springs, strings and gears. Tricks for amplifying force are usually based on principles idealized by pulleys, levers, wedges and toggles. Analysis of force transmissions and mechanisms is done by visualizing free-body picture of the parts and writing equations and solving the equations for desired unknowns in equilibrium.

Hydrostatic is majorly concerned with force and moments. Pressure increases with depth. With constant pressure, the equivalent force has magnitude = pressure times area, acting at the centroid. For linearly-varying pressure on a rectangular plate the equivalent force is the average pressure times the area acting somewhere between 1/2 and 2/3 of the way down. The net force acting on a totally submerged object in a constant density fluid is the displaced fluid's weight, acting at the centroid.

The ideal harmonic oscillator (previous chapter) oscillates with simple sinusoidal motion forever. In the real world there is friction so oscillations decay more or less quickly, there are forces that cause the oscillations, and there are multiple parts that move multiple ways.

The components for statics like relative position, force, and moment etc. are used to develop vector skills. An idea for static and dynamic is proposed because identification find vectors from scalars or they separate vectors from scalars Vector addition means to add forces and relative positions. Dot products the tool which transforms the base equation to a new equation. Cross products are the formula which correctly calculates the heuristically motivated quantities of moment and moment about an axis.

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