Static Equilibrium and tension of cables

In summary, the problem is to calculate the tension in each cable of a suspended neon sign with three cats (5.0 Kg each) sitting on it. The centre of mass is found using the given equations and the tension in each cable is determined by summing torques about the base of the sign. The final result is that one cable has a tension of 250.8N while the other has a tension of 190.4N.
  • #1
Juniper7
19
0

Homework Statement


A 30Kg neon sign is suspended by two cables, as shown. Three neighbourhood cats (5.0 Kg each) find the sign a comfortable place. Calculate the tension in each cable with the cats are in the positions shown.


Homework Equations



xCM = m1x1 + m2x2 ...
mtotal

yCM = m1y1 + m2y2 ...
mtotal

F = mg

The Attempt at a Solution



I found the centre of mass (CM) by assigning each cat a coordinate using the bottom left corner of the sign as the origin with (x,y). So:

Cat1 = (0.2,0.5)
Cat2 = (1.8,0.5)
Cat3 = (2,0)
Sign = (1,0.25) --> the centre of the sign

Using the above two equations I found the centre of mass of the cats and sign to be (1.11m,0.278m)

There should be no forces in the x-axis and the forces in the y-axis should all cancel out so:

T1cable + T2cable = mg

I know the position of each cable from the picture so: (using only y-axis position)

T1(0.5m) + T2(0.5m) = (45kg)(9.81)(0.278m)

The tension in each cable should be equal? Or, because one cable is farther from the CM it should have less tension? Does this mean I should be taking into account the x axis? Please help!
 

Attachments

  • Screen Shot 2014-05-27 at 4.15.58 PM.png
    Screen Shot 2014-05-27 at 4.15.58 PM.png
    4.6 KB · Views: 506
Last edited:
Physics news on Phys.org
  • #2
Looks like you y'd when you should have x'd. Torque is force times perpendicular distance from line of action of force to any point chosen wisely.
 
  • #3
Hm ok. So:

T1(0.2m) + T2(1.8m) = (45kg)(9.81m/s2)(1.11m)

T = 245N

So that means each cord has a tension of 245N?
 
  • #4
Juniper7 said:
Hm ok. So:

T1(0.2m) + T2(1.8m) = (45kg)(9.81m/s2)(1.11m)

T = 245N

So that means each cord has a tension of 245N?
No, your equation was ok but then you assumed that T1 and T2 were equal and got an erroneous result. To simplify matters, try summing torques not about your assumed origin at (0,0), but rather, about the point at the base of the sign at coordinate (0.2,0). You can choose any point, but keep it simple. In this manner, you can solve for T2 directly, because there will be no torque from T1, then continue...
 
  • #5
PhanthomJay said:
No, your equation was ok but then you assumed that T1 and T2 were equal and got an erroneous result. To simplify matters, try summing torques not about your assumed origin at (0,0), but rather, about the point at the base of the sign at coordinate (0.2,0). You can choose any point, but keep it simple. In this manner, you can solve for T2 directly, because there will be no torque from T1, then continue...

Ok. So coordinates for each point would be in relation to (0.2,0) If I do it how you suggest:

T1(0m) + T2(1.6m) = (45kg)(9.81m/s2)(0.91m)

T2 = 250.8N

Then can I use my earlier equation to solve for T1?

T1(0.2m) + T2(1.8m) = (45kg)(9.81m/s2)(1.11m)
0.2T1 + (250.8N)(1.8m) = (45kg)(9.81m/s2)(1.11m)
T1 = 190.4N
 
  • #6
You look to be correct. I worked it out separately and got this result, so I hope you're right :p.
 
  • #7
Crush1986 said:
You look to be correct. I worked it out separately and got this result, so I hope you're right :p.
yes, looks good!
 
  • #8
Thanks!
 

1. What is static equilibrium?

Static equilibrium is a state in which all forces acting on an object are balanced and the object is at rest or moving at a constant velocity.

2. How is tension of cables calculated?

The tension of a cable can be calculated using the formula T = mg + ma, where T is tension, m is mass, g is acceleration due to gravity, and a is acceleration.

3. What factors affect static equilibrium?

The factors that affect static equilibrium include the weight and mass of the object, the angle and direction of forces acting on the object, and the coefficients of friction between the object and its supporting surface.

4. How does the angle of a cable affect tension?

The angle of a cable can affect the tension by increasing or decreasing the vertical and horizontal components of the tension force. As the angle increases, the horizontal component of tension decreases while the vertical component increases.

5. What is the difference between static and dynamic equilibrium?

Static equilibrium is a state of balance in which the object is at rest or moving at a constant velocity, while dynamic equilibrium is a state of balance in which the object is moving with a constant velocity in a straight line.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
949
  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
12
Views
5K
  • Introductory Physics Homework Help
Replies
7
Views
13K
Back
Top