Help finding Tension on a hanging bag

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In summary, the homework statement says that if a bag of cement of weight Fg hangs from three fires, the tension in the left hand wire is T1 = Fgcos(theta2)/sin(theta1 + theta2).
  • #1
szimmy
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Homework Statement


FBD: http://i560.photobucket.com/albums/ss45/ZimmyGFX/photo.jpg
A bag of cement of weight Fg hangs from three fires as shown in the figure. Two of the wires make angles theta1 and theta2 with the horizontal. If the system is in equilibrium, show that the tension in the left hand wire is T1 = Fgcos(theta2)/sin(theta1 + theta2)


Homework Equations


T1cos(theta1) - T2cos(theta2) = 0
T1sin(theta1) + T2sin(theta2) = Fg (aka T3)


The Attempt at a Solution


Using the equation T1sin(theta1) + T2sin(theta2) = Fg I was able to single out T2 to plug into the other equation (since I'm solving for T1).
T2 = (Fg - T1sin(theta1))/sin(theta2) is what I got
Then I substituted T2 for the equation found into T1cos(theta1) = T2cos(theta2) because the system is at equilibrium in the x direction.
So I get T1cos(theta1) = ((Fg - T1sin(theta1))/sin(theta2)) * cos(theta2)
Simplifies to T1cos(theta1) = (Fgcos(theta2) - T1sin(theta1)cos(theta2))/sin(theta2)
I then divide off cos(theta1) and get the following
T1 = (Fgcos(theta2) - T1sin(theta1)cos(theta2))/(sin(theta2)cos(theta1))

This isn't what I'm supposed to get though. I still have a T1 on both sides of the equation but if I divide it over then it will cancel off.
I'm supposed to be getting Fgcos(theta2)/sin(theta1 + theta2)
and sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
I have all the elements for the denominator on the right side, but two are on top and should be on the bottom.
I obviously messed up big time somewhere, but I'm stuck and don't know where to go from here.
 
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  • #2
You're doing fine. On the left hand side, you have one term that is a multiple of T1. On the right hand side, you have a term that is not a multiple of T1 minus a term that is a multiple of T1. In other words, you've got something that looks like 5x=2-3x. How would you solve that?
 
  • #3
Ibix said:
You're doing fine. On the left hand side, you have one term that is a multiple of T1. On the right hand side, you have a term that is not a multiple of T1 minus a term that is a multiple of T1. In other words, you've got something that looks like 5x=2-3x. How would you solve that?

Yeah I took a look back right before you posted that and I realized I wasn't done simplifying. I didn't take a deep enough look at it and at first glanced I figured that I would end up with a 2T1 or something, not that it would factor out. I guess I should have worked it out instead of being lazy next time. Thanks anyway though
 

Related to Help finding Tension on a hanging bag

1. How do you find the tension on a hanging bag?

To find the tension on a hanging bag, you will need to use the equation T=mg, where T is the tension, m is the mass of the bag, and g is the acceleration due to gravity (9.8 m/s²).

2. What tools are needed to measure the tension on a hanging bag?

The tools needed to measure the tension on a hanging bag include a scale to measure the mass of the bag, a ruler to measure the length of the hanging string, and a calculator to calculate the tension using the equation T=mg.

3. What factors can affect the tension on a hanging bag?

The factors that can affect the tension on a hanging bag include the mass of the bag, the length of the hanging string, and the acceleration due to gravity. Other factors such as wind or movement of the bag may also affect the tension.

4. How can you increase the tension on a hanging bag?

To increase the tension on a hanging bag, you can either increase the mass of the bag or decrease the length of the hanging string. Both of these factors will increase the force of gravity acting on the bag, thus increasing the tension.

5. What is the importance of finding the tension on a hanging bag?

Knowing the tension on a hanging bag is important in various situations such as construction, sports, or scientific experiments. It helps in determining the stability and strength of the bag and ensures that it can hold the desired weight without breaking or causing any accidents.

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