Kinetics of a particle, Mechanical Engineering

Kinetics of a Particle:

We have seen the effect of forces on a particle. The laws of motion for a particle are extended to include a system of particles or a rigid body. It is done by using D′Alembert's principle. D′Almbert's principle states that the resultant of forces acting on a body is equivalent to the sum of the effective forces acting on all of the particles of the body.

Further, we may say that while forces are acting on the particles of a body, we may imagine inertia forces also acting on the particles bringing the body in dynamic equilibrium. This principle may be extended further to find out the motion of mass centre of any body. We understand that the resultant of the applied external forces is equal to the product of the mass of the body and the acceleration of its mass centre which is expressed as F = ma.

The motion of translation of a rigid body is described as a motion in which a straight line passing through any two particles of a body is always parallel to its initial position. Further, we may say that the translation of a rigid body is equivalent to that of a particle having the mass of the body and the motion of the mass centre of the body.

For rectilinear motion, Consider x axis be directed along the initial direction of motion, and reckoned as positive. Then we can write the equations as below,

∑ Fx  = ma.

∑ Fy  = 0,       ∑ Fz  = 0

 For curvilinear motion, normal and tangential components of acceleration (N and T, respectively) are utilized to write equations.

∑ F n = m an  = m (v2/r)

∑ Ft = m at = m( dv/ dt)

The problem becomes very simple while inertia reactions of magnitudes m v 2 /r and m . dv/ dt are applied via the mass centre and directed opposite to the normal and tangential components of acceleration respectively and dynamic equilibrium equations are written.

The advantage of dynamic equilibrium is that all the methods of statics may be applied to a single free body diagram which includes the components of inertial reaction ma. This is very much useful while moment summation is calculated at a centre which is the intersection of two unknown forces and set to zero.

Posted Date: 1/29/2013 12:32:54 AM | Location : United States







Related Discussions:- Kinetics of a particle, Assignment Help, Ask Question on Kinetics of a particle, Get Answer, Expert's Help, Kinetics of a particle Discussions

Write discussion on Kinetics of a particle
Your posts are moderated
Related Questions
Thermodynamics. Justify that it is the science to calculate energy, energy and entropy. Sol : Thermodynamics is science which deals with conversion of heat into mechanical e

(a) Describe and calculate i) Humidity Ratio ii) DPT iii) Relative Humidity iv) Density v) Enthalpy of atmosphere air when DBT is 35 0 C, WBT is 23 0 C and the ba

i have an assignment due tomorrow

1- Explain the rationale of using a small WD to improve resolution. 2- In a tungsten SEM , Why does a high accelerating voltage provide the potential for higher resolution?  Why

A centrifugal clutch is to be prepared to transmit 15 KW at 900 r.p.m. The shoes are four in number. The speed at which the engagement begins is 3/4 th of the running speed. The in

Give differences between direct stress and bending stress. Direct tensile and compressive stress is set up because of load applied parallel to length of object, and direct shea

Flux Cored Arc Welding (FCAW) This is a variation of GMAW where solid wire is replaced by flux cored wire. The equipments and accessories are the same. Generally, flux cored wi

Compressive Stress: The stress induced in a body, when subjected to two equal and opposite pushes as shown in figure (a) as a result of which there is an decrease in length

Find the value of force to move a system: Th e system of particles shown in the figure given below is initially at rest. Find the value of force F which should be applied so

Parts of Aircraft  The main parts of an aircraft are (Figure): (a) Engine, which propels the aircraft; the aircraft may have jet engines or propeller driving engines. (b