Equilibrium question on review assignment, quick (I have a test tomorrow).

[StaticWaffles]

Homework Statement

A rod of negligible mass is supported by a hinge at the wall by a horizontal wire fastened at a 30 degree angle one-third of the way along the rod. A weight of 12 N hangs from the left end of the rod.

a) Find the tension (T) in the horizontal wire. (T = 62.2 N)
b) Find the magnitude and direction of the force that the hinge exerts on the end of the rod. (FH = 63 N, 11 degrees NW)

Homework Equations

Sum of the Torques clockwise = Sum of the torques counterclockwise (ETcw = ETccw)
Basic trig like sin, cos and tan.

The Attempt at a Solution

I solved a) already.
(Tcos60*1/3d) = (12cos30*d)
(T*0.1666666) = (10.39230485)
T= 62.3 N

(Here is a picture of the diagram; it's not very clear)
http://twitpic.com/bzeo8w
The angle the wire makes with the rod is 30 and the angle the weight makes with the rod is 60.
Question b) however I am completely stuck on, it would be great if someone could explain how to do it step by step.
http://twitpic.com/bzeo9g
I tried to find FHy and FHx however nothing made sense to me and I've spent three hours on this.

 

[SammyS]

Homework Statement

A rod of negligible mass is supported by a hinge at the wall by a horizontal wire fastened at a 30 degree angle one-third of the way along the rod. A weight of 12 N hangs from the left end of the rod.

a) Find the tension (T) in the horizontal wire. (T = 62.2 N)
b) Find the magnitude and direction of the force that the hinge exerts on the end of the rod. (FH = 63 N, 11 degrees NW)

Homework Equations

Sum of the Torques clockwise = Sum of the torques counterclockwise (ETcw = ETccw)
Basic trig like sin, cos and tan.

The Attempt at a Solution

I solved a) already.
(Tcos60*1/3d) = (12cos30*d)
(T*0.1666666) = (10.39230485)
T= 62.3 N

(Here is a picture of the diagram; it's not very clear)
http://twitpic.com/bzeo8w
The angle the wire makes with the rod is 30 and the angle the weight makes with the rod is 60.
Question b) however I am completely stuck on, it would be great if someone could explain how to do it step by step.
http://twitpic.com/bzeo9g
I tried to find FHy and FHx however nothing made sense to me and I've spent three hours on this.

There are only three forces acting on the rod:

The weight hanging from the end.

The tension of the wire.

The force exerted by the hinge.​

It's a fairly straight forward equilibrium problem .

 

[StaticWaffles]

There are only three forces acting on the rod:

The weight hanging from the end.

The tension of the wire.

The force exerted by the hinge.​

It's a fairly straight forward equilibrium problem .

I know but I don't know why the answer is 11 degrees NW, that's where I am confused.

 

[SammyS]

I know but I don't know why the answer is 11 degrees NW, that's where I am confused.

In my opinion, using a compass direction here is rather strange.

I get the the hinge exerts a force of 63.347 Newtons outward from the wall at an angle of 10.9197° above the horizontal. If that's considered NorthWest, then fine.

 

[StaticWaffles]

In my opinion, using a compass direction here is rather strange.

I get the the hinge exerts a force of 63.347 Newtons outward from the wall at an angle of 10.9197° above the horizontal. If that's considered NorthWest, then fine.

How do you get 63.347 N for the force that the hinge exerts? Sorry for asking all these questions, this question is just really confusing me though.

 

[SammyS]

How do you get 63.347 N for the force that the hinge exerts? Sorry for asking all these questions, this question is just really confusing me though.

$\displaystyle 63.347\approx\sqrt{62.2^2+12^2\,}$

 

[StaticWaffles]

$\displaystyle 63.347\approx\sqrt{62.2^2+12^2\,}$

Thank you so much!