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

In summary: That makes sense now.In summary, a rod of negligible mass is supported by a hinge and a horizontal wire, with a weight of 12 N hanging from one end. The tension in the wire is 62.2 N and the force exerted by the hinge on the end of the rod is 63.347 N at an angle of 10.9197° above the horizontal.
  • #1
StaticWaffles
8
0

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.
 
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  • #2


StaticWaffles said:

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 .
 
  • #3


SammyS said:
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.
 
  • #4


StaticWaffles said:
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.
 
  • #5


SammyS said:
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.
 
  • #6


StaticWaffles said:
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.
[itex]\displaystyle 63.347\approx\sqrt{62.2^2+12^2\,}[/itex]
 
  • #7


SammyS said:
[itex]\displaystyle 63.347\approx\sqrt{62.2^2+12^2\,}[/itex]

Thank you so much!
 

1. What is equilibrium?

Equilibrium is a state in which opposing forces or influences are balanced, resulting in a stable and unchanging system.

2. How is equilibrium achieved?

Equilibrium is achieved when the rate of the forward reaction is equal to the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products.

3. What factors can affect equilibrium?

The factors that can affect equilibrium include changes in temperature, pressure, and concentration of reactants or products. Adding or removing a reactant or product can also shift the equilibrium.

4. How can we calculate equilibrium constants?

Equilibrium constants can be calculated using the concentrations of reactants and products at equilibrium, as well as their stoichiometric coefficients in the balanced chemical equation.

5. How do we know when a system is at equilibrium?

A system is at equilibrium when the concentrations of reactants and products remain constant over time, there is no observable change in the physical properties of the system, and the rate of the forward and reverse reactions are equal.

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