Mechanics Caltec S.5

MECHANICS This is a branch of physics which deals with the action of forces on bodies. Branches of mechanics: Dynamics Statics Hydrodynamics Hydrostatics Dynamics: This is a branch of mechanics which deals with solids in motion Static: This deals with solid bodies at rest Hydrodynamics: This deals with liquids or fluids in motion Hydrostatics: It deals with fluids at rest Physical quantities Physical quantities can be divided into two groups i.e. Fundamentalquantities: Theseare physical quantities which cannot be expressed in terms of other quantities using any other mathematical means; for example Length (L), Mass (M), Time (T) and Temperature Dimensional/derivedquantities:These are physical quantities which can be expressed in terms of the fundamental quantities e.g. power, force, work, area, volume, density, speed, acceleration and momentum. Dimensions of physical quantity This is the way a derived physical quantity is related to the fundamental quantities of mass, length and time. Square brackets, [ ] are used to show dimensions. Examples [Mass] = M [Length] = L [Time]= T Area = length × length or length × width = = [Volume]= = . [Density] = = [Force] = [mass] × [acceleration] = [Speed] = = [Surface tension]= Uses of dimensions To check the validity of equations (equations which are not dimensionally consistent are obviously wrong expressions and should be discarded. To drive equations. Checking validity of equations for current equation, the units on the left hand side must balance with those on the right hand side. Similarly, [L.H.S] = [R.H.S] All right equations must be dimensionally consistent but not all dimensionally consistent equations are correct. Examples The centripetal force F on a body of massM moving at a constant speed V round a circular path of radius r is given by Show that the equation is dimensionally consistent. Solution Force=Ma but F=Ma [.LH.S]= [force] …