Static Equillibrium. [T=0, [F=0? Problem finding force using component

In summary, the student found that the resultant force was 1637 N, which was larger than the force exerted at the hinge, meaning that the beam might not be stable at that angle.
  • #1
hangingwire
8
0
Taking a physics 12 class in night school and he only gave us an example of a Beam and Wire question where the Wire was holding a Beam against a wall. The wire was at the end of the beam and holding a sign.

Using the methods taught, I have been able to understand the Torque = 0, but Forces get me stuck

This is a nifty site and my next class (and unit test) is on Tuesday. Teacher hardly checks emails!

Homework Statement


Find the cord tension and force from hinge on this beam.

Hinge is at the wall. Beam is 4.50m long. Object at end is 20 kg heavy. The beam is 80kg. Also, the wire this time is 1.0m from the end (**star** is the wire) with an angle of 25 degrees.

H.______*__

Homework Equations



Sum of T = 0
Sum of F = 0

The Attempt at a Solution



First using the sum of Torques:
Tcw = TccwClockwise applications:
Mb*G (Beam)
Mo*G (Object)

Counter-cw:
Ty

Using all these applications and their distances relative to the pivot (Pivot @ H)
Mb*G*d + Mo*G*d = Ty*d
(80)(9.8)(2.25m) + (20)(9.8)(4.5m) = Tsin25 * (3.5m)
1764 + 882 = (3.5) * Tsin25

Divide by 3.5

756 = Tsin25

Divide by sin25

T = 1788.8N --> 1790N (The answer is rounded in my book)Now for forces.

Fx = 0
FHx - Tx = 0
FHx = Tx
FHx = Tcos25
FHx = 1790cos25
FHx = 1622.3N

But the answer is 1600N. Using pythagorean theorem, the x is larger than the resultant?
 
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  • #2
I can't see an error in your working.

The vertical component at the hinge isn't zero so it's not just 1622 rounded down to 1600N. I make the resultant about 1800N so could be a typo ?
 
  • #3
I understand that there is a Y component but I stopped after I saw FHx = 1622N

From my understanding... The answer should be 1637N (I had a friend who is into math, calculus and taking engineering in university see if I made an error after posting this?)
He got the same 1637N as me

[Fy=0
FN+Ty(up)+F1g (down)+F2g(down)=0
FN + 1790sin25 + (-784) + (-196) = 0

Flipping over some question to the other side

Fn = 784 + 196 - 756
Fn = 224

R= Sq. Root {1622^2 + 224^2)
R= 1637N

Tan-1(224/1622)
Angle = 7.86 degrees (the angle is 7.87 in answer?)

So I am assuming that they just rounded down to 1600N?
 
  • #4
Yes looks like misscalculated. I agree with your figure of 1637N.
 
  • #5
I emailed my teacher it is correct, rounded to 2 sig figs. Thanks for helping out! I'm on to beams at angles now so if I need any more help I shall ask on here :)

Just wondering, this is a physics forum with some advanced applications all over mathematics. Would physics 12 fit in this introductory physics all the way through?
 

1. What is static equilibrium?

Static equilibrium is a state in which an object is at rest and all forces acting on the object are balanced, resulting in a net force and net torque of zero.

2. What does T=0 mean in the context of static equilibrium?

In the context of static equilibrium, T=0 refers to the sum of all torques acting on an object being equal to zero. This means that the object will not rotate or spin due to the balanced torque forces.

3. What does F=0 mean in the context of static equilibrium?

In the context of static equilibrium, F=0 refers to the sum of all forces acting on an object being equal to zero. This means that the object will not move or accelerate in any direction due to the balanced forces.

4. How do you find the force using components in a static equilibrium problem?

To find the force using components in a static equilibrium problem, you can use the principle of moments, which states that the sum of the clockwise moments must equal the sum of the counterclockwise moments. This can help you determine the magnitude and direction of the force needed to achieve static equilibrium.

5. What is the importance of static equilibrium in science and engineering?

Static equilibrium is important in science and engineering because it allows us to analyze and understand the forces and torques acting on objects in a state of rest. This knowledge is crucial in designing stable structures and predicting the behavior of objects in various situations.

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