a the minimum value of vector Fis N b the normal force exert

(a) the minimum value of vector Fis? N

(b) the normal force exerted by the incline on theblock? N

The component F cos acts parallel tothe plane ( towards right side ) and

the component F sin acts perpendicular tothe plane ( downward )

Normal reaction, N = mg cos + F sin

frictional force, f = N = ( mg cos + F sin )

Condition for equilibrium, Net force along the plane inupward direction =

Netforce along the plane in downward direction

Fcos = ( mg cos + F sin ) +mg Sin

F ( cos - Sin ) = mg ( Sin + cos )

(a) Minimum value of F = mg ( Sin + cos ) / ( cos - Sin ) = 27.2N

(b) Normal force, N = mg cos + Fsin = 33.4 N