A block of mass of 2 kg slides on an inclined plane that makes an angle of 30 % with the horizontal . The coefficient of friction between the block and the surface is `(sqrt(3))/2 ` .
(a) What force should be applied to the block so that it moves up without any acceleration ?
(b) What force should be applied to the block so that it moves up without any acceleration ?

Explanation

m = 2 kg ` theta = 30^(@) , mu = (sqrt(3))/2 `
(i) `F_(down) = mg (sin theta - mu cos theta )`
` = 2 xx 9.8 ( sin 30 ^(@) - (sqrt(3))/2 cos 30^(@))`
` = 2 xx 9.8 ( sin 30^(@) - (sqrt(3))/2 cos 30^(@))`
` = 2 xx 9.8 [ 1/2 - (sqrt(3))/2 xx (sqrt(3))/2] = 4.9 N `
(ii) `F_(up) = mg( sin theta + mu cos theta )`
` = 2 xx 9.8 [ sin 30^(@) + (sqrt(3))/2 xx cos 30^(@)] `
` = 2 xx 9.8 [ 1/2 + (sqrt(3))/2 xx (sqrt(3))/2 ] = 24.5 N `