Kinetics of a particle, Mechanical Engineering

Assignment Help:

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.


Related Discussions:- Kinetics of a particle

About Transfer Function block, How can i change the normal function block p...

How can i change the normal function block parameter[1 1]=>(s+1) to (s-1)?

Erosion-corrosion in steam service, Q.What is Erosion-Corrosion in Steam Se...

Q.What is Erosion-Corrosion in Steam Service? Depending on the steam quality, Let-down valves are subject to erosion-corrosion when pressure drop exceeds 1000kPa. Hard facing i

Types of registration in entrepreneurship development, Types of Registratio...

Types of Registration Provisional Registration Certificate ( PRC ) This is given for the pre-operative period and enables the units to obtain the term loans and worki

Theory of machines, What'' is balancing and vibration in machines Need of ...

What'' is balancing and vibration in machines Need of balancing? Causes of vibration and their harmful effects and remedies?

Thermodyamics, work is path function not a state function

work is path function not a state function

Uniformly distributed load and uniformly varying load, Uniformly Distribute...

Uniformly Distributed Load and Uniformly Varying Load: Uniforml y Distributed Load (UDL) A UDL is one which is spread over beam in such a manner that the rate of loading

Tom, ‘coefficient of insensitiveness’ of governors

‘coefficient of insensitiveness’ of governors

Design of a filament winding machine, How can I achieve a back and forth mo...

How can I achieve a back and forth movement of carriage system. How can I reverse the motor to go back and forth.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd