a body is in limiting equilibrium on a rough inclined plane at angle of 30degree with horizontal. calculate the acceleration with which the body will slide down when inclination of the plane is changed to 60degree.?

1 Answer
Jul 19, 2017

In first case when the body is in limiting equilibrium at angle of inclination of the inclined plane, 30^@
then the downward force along the inclined plane is just balanced by the frictional force ,. So we have

mgsintheta =mumgcostheta

mu =sintheta/costheta=tan30^@=1/sqrt3,

where

m->"mass of the body"

theta ->"angle of inclination of the inclined plane"=30^@

mu->"coefficient of friction"

g->"acceleration due to gravity"

In the second case when the angle of inclination is theta=60^@ we have net downward force on the body along the inclined plane

F=mgsintheta-mumgcostheta

So acceleration of the body

a=F/m=g(sintheta-mucostheta)

=g(sin60^@-1/sqrt3cos60^@)

=g(sqrt3/2-1/sqrt3xx1/2)

=g/2(sqrt3-1/sqrt3)

=g/2((3-1)/sqrt3)=g/sqrt3