In figure the uniform gate weights `300N` and is `3m` wide `& 2m` high. It is supported by a hinge at the bottom left corner and a horizontal cable at the top left corner, as shown. Find `:`
`(a)` the tension in the cable and
`(b)` the force that the hinge exerts on the gate `(` magnitude `&` direction `)`.

Answer

`(a)T=225N,(b)F_(x)=225N,F_(y)=300N`

Explanation

From `FBD`
Equation in horizontal direction
`T=Nx ……(1)`
For Rotational equation about `P`
`T.2=1.5xx300`
`T=225N`
`N_(x)=225N`
`N_(y)=300N`
And `Ng=mg=300N`