Derive an expression for the acceleartion of the bodysliding down a fr

1.	Derive an expression for the acceleartion of the bodysliding down a frictionless surface
Answer» Solution :Whenan objectof massmslideson africtionalsurfaceinclinedat anangle `theta` as shownin the figurethe forcesactingonitdecides theaccelerationof THEOBJECT(b)speedof theobject when it reachesthe bottom . The forceactingon theobject is (i)Downwardgravitational force (mg) (II) Normalforceperpendicularto inclinedsurface (N) theblockis assumedto be apointmass[Inorder to drawthe freebodydiagram in figure(a)].Sincethe motionis on theinclinedsurfacethecoordinatesystemparallelto tehinclinedsurfaceis chosenas shown in thefigure (b)It isnotedthat theanglemadebythe gravitationalforcewith theperpendicularto the surfacesi EQUALTO theangleof inclination `theta` as shown inin figure `-mg cos theta hat(j)+ N hat(j) = 0`(No acceleration ) Bycomparingthecomponentson bothsidesN- mg cos `theta = 0` `N= mg cos theta` Themagnitude of normalforce(N)exertedby tghesurfaceis EQUIVALENTTO mgcos `theta` . Theobjectslidesalongthe x direction . Bycomparingthe componentson bothsideswe canequate `mg sin theta= ma ` Theaccelerationof theslindingobjectis Notethat theacceleratindependson theangleinclination `theta`

Derive an expression for the acceleartion of the bodysliding down a frictionless surface