A body of mass 2 kg is lying on rough inclined plane of inclination 30 degree . Find the magnitude of the force parallel to the incline needed to make the block move a. up the incline b. down the incline. Coefficient of static friction =0.2
Repeat part a. of problem 6 if the push is applied horizontally and not parallel to the incline.

Explanation

From te free body diagram,

`g=10 m/s^2`
`m=2kg`
`theta=30^0, m,u =0.2`
From `R-mg cos theta-F sin theta =0`
`rarr R=mg costheta+F sin theta `……..i
and `mg sintheta +mu R-F cos theta=0`
`rarr mg sin theta+mu (mg costheta+Fsin theta)-F cos `
`theta=0`
`rarr mg sin theta +mu mg costheta +mu F sin theta -Fcos theta =0`
`rarr F=((mg sin theta+mu costheta))/(mu sintheta-costheta)`
`=((2xx10xx(1/2)+0.2xx2xx10xxsqrt3/2))/(0.2xx(1/2)-(sqrt3/2)`
`=13.464/0.76=17.7N=17.5N`