Solve Farm Gate Problem: Horiz Force on Bottom Hinge

[xRandomx210]

Old MacDonald had a farm, e i , e i , oh ! And
on that farm he had a gate, e i , e i , oh ! And
a squeak, squeak, here. A squeak, squeak,
there. And a squeak, squeak, everywhere . . .
The gate is ℓ = 3 m wide and h = 2.47 m
tall with hinges attached to the top and bot-
tom. The guide wire makes an angle of
α = 39 ◦ with the top of the gate and has
a tension of 221 N. The mass of the gate is
30.9 kg.

Determine the magnitude of the horizon-
tal force exerted on the gate by the bottom
hinge. The acceleration of gravity is 9.8 m/s2 .
Answer in units of N.

Okay the reason why I am having problems with this is because well I am just not sure I know where to start. I think I am just missing something obvious, and my book does not have a whole lot to say about this type of problem. Any Help?

 

[tiny-tim]

Hi xRandomx210!

(ooh, that gate is really annoying … if i help with the question, will you please oil it?)

There are only four external forces on the gate.

You know 2 of them, and you want one of them, but you don't know the fourth one, and and you don't want to know it, so … standard trick … take moments about the point of application of that unknown force.

 

[xRandomx210]

Sorry for being a noob, but what does oiling it mean?

 

[xRandomx210]

Just tried something, don't know if it is right or not.

Σfx= TCos(Theta) = H1x+H2x

where Hx is the force of the hinge in the x direction

Σfy=TSin(theta) + Hy1 + Hy2 = mg

ΣT = mg(L/2)-Tsin(theta)L= Hx(h)

from there you can slove out, but is the method correct?

 

[xRandomx210]

Never mind the reason i got it wrong the first time was because i used 9.81 instead of 9.8 :C