Static equilibrium: calculating force of tension

In summary: The final result will be the same either way you calculate it. The method you used is simpler, but it's always good to be aware of alternative methods. In summary, the system is in static equilibrium with the string in the middle being exactly horizontal. The tension in each string (T1, T2, and T3) can be calculated using trigonometric equations and the given information. The angle of the tension vector (theta) can also be calculated using trigonometric identities and equations.
  • #1
janelle1905
25
0

Homework Statement


The system (picture found in attachment) is in static equilibrium, and the string in the middle is exactly horizontal.
Find
a. Tension T1
b. Tension T2
c. Tension T3
d. angle (theta)

Homework Equations


sin=opp/hyp
cos=adj/hyp

The Attempt at a Solution


a. Using Ty = T1sin60 - mg = 0, T1=34 N.

b. Using Tx = T2 - T1cos60 = 0, T2 = 17 N

c. Eq'n 1: Tx = T3sin(theta) - mg = 0
Re-arranged to: theta = cos-1 T2/T3

Eq'n 2: Ty = T3sin(theta) - mg = 0

Then I substituted the re-arranged eq'n (1) into eq'n (2), and I got this:
0 = T3sin(cos-1 T2/T3) - mg

However, I don't know how to solve this ... so I think I may be doing something wrong.

Thank you in advance for any assistance!
 
Physics news on Phys.org
  • #2
Sorry, there is no attachment that I can see and without it I don't want to guess at what the picture looks like.
 
  • #3
Very sorry about that!
I have added the attachment to this post...hopefully it works this time!
 

Attachments

  • staticequilib2.jpg
    staticequilib2.jpg
    6.2 KB · Views: 702
  • #4
Parts (a) and (b) look OK.

Part (c)
If you draw the FBD for the mass m2, you get

T3sinθ - m2g = 0
- T2+T3cosθ = 0

So T3sinθ = m2g

and

T3cosθ = T2

These are the horizontal and vertical components of the tension. Can you find its magnitude?
 
  • #5
Thanks so much for your help :)

Using the following equations:

1. T3sinθ - m2g = 0
2. - T2+T3cosθ = 0

I re-arranged and substituted eq'n 1 into 2, and then calculated theta=49o.
The only thing I wasn't sure about was when I had cos(theta)/sin(theta), I simplified it to 1/tan(theta). Is this the correct was to use the trig identity tan=sin/cos ??

Then I substituted the calculation for theta to calculate T3=26 N.
 
  • #6
Your method is fine. What I was hinting at is that if you know the x and y components of T3, then the magnitude is given by

T3=[T3x2+T3y2]1/2 = [(m2g)2+(T2)2]1/2

and, as you pointed out, you get the angle from

tanθ = T3y / T3x = m2g / T2
 
  • #7
Okay I see what you were saying - but you get the same answer either way, correct?
 
  • #8
Correct.
 

What is static equilibrium?

Static equilibrium is a state where all forces acting on an object are balanced, resulting in no net acceleration or movement of the object.

How is static equilibrium calculated?

The principle of static equilibrium states that the sum of all forces acting on an object must be equal to zero. Therefore, to calculate static equilibrium, we must analyze the forces acting on the object and determine their magnitudes and directions.

What is the force of tension?

The force of tension is a pulling force that is exerted by a string, rope, or cable on an object. It is always directed along the length of the string and away from the object.

How do you calculate the force of tension?

The force of tension can be calculated using the formula F = mg + ma, where F is the force of tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object. This formula assumes that the object is in static equilibrium.

What are some real-world applications of calculating force of tension in static equilibrium?

Calculating the force of tension in static equilibrium is essential in many engineering and physics fields. For example, it is used in bridge construction to determine the strength of cables and support structures. It is also used in rock climbing to ensure the safety of climbers and their equipment.

Similar threads

  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
945
  • Introductory Physics Homework Help
Replies
2
Views
844
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Introductory Physics Homework Help
Replies
12
Views
3K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top