A uniform rod of mass `m` and length `L` is held at rest by a force `F` applied at it's end as shown in the vertical plane. The ground is sufficienty rough Find -
(a) Force `F`
(b) Normal reaction exerted by the ground
( c) Friction force exerted by the magnitude and direction).
.

Answer

(a) `(mg cos alpha)/(2)`
(b) `mg(1 - (cos^(2) alpha)/(2))`
( c) `(mg sin alpha cos alpha)/(2)`

Explanation

(a) Taking rotational equilibrium about point of contact.
`FL = mg cos alpha xx (L)/(2)`
`F = (mg)/(2) cos alpha`

(b) For translational equilibrium in vertical direction.
`F cos alpha + N = mg`
`N = mg - F cos alpha rArr N = mg (1 -(cos^(2) alpha)/(2))`
( c) Taking translational equilibrium inhorizontal direction.
`F_(r) =F sin alpha rArr F_(r) = (mg)/(2) cos alpha sin alpha`.