A `30kg` box has to move up an inclined plane of slope `30^(@)` the horizontal with a unform velocity of `5 ms^(-1)`. If the frictional force retarding the motion is `150N`, the horizontal force required to move the box up is `(g =ms^(-2))` .

Explanation

The force required to move a body up an inclined plane is
`F=mg sintheta+f_(k)`
`f_(k)=mu_(k)(mg cos theta+P sin theta)=150N`
`=30(10)sin 30^(@)+150=300N`.
If P is the horizontal force, `F=P cos theta`
`P=(F)/(cos theta)=(300)/(cos 30^(@))=(300xx2)/(sqrt3)=200sqrt3=346N`