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
P dilip_k
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#

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