Solving for Tension in Cement Bag Wires

In summary, using Newton's Laws of motion and the given angles, we can determine the tensions in the wires supporting a 350 N bag of cement. By breaking up the tensions into their vertical and horizontal components and setting them equal to the weight and to each other, we can form a system of equations to solve for T1 and T2.
  • #1
intriqet
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Homework Statement



A bag of cement of weight 350 N hangs from three wires as suggested in the figure below. Two of the wires make angles θ1 = 50.0° and θ2 = 27.0° with the horizontal. Assuming the system is in equilibrium, find the tensions in the wires.



Homework Equations



Newton's Laws of motion

The Attempt at a Solution



I know that the tension for T3 is just equal to the weight. But how do I split the force between the remaining two strings?
 

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  • #2
Find the vertical and horizontal components of T1 and T2.
In equilibrium condition, Vertical components add up to ...?
What happens to horizontal components?
Solve these two equations to find T1 and T2.
 
  • #3
Please pardon my stupidity. How would I break up T1 and T2 into components? My first impulse was to do 350costheta and 350sintheta for each tension force and its respective theta but that's obviously not the way to go.

I also figured that if the system was in equilibrium. F1total + F2total + F3total = 0, but I have no idea where to go from there because I still have 2 unknowns and only 1 equation
 
  • #4
The vertical components are T1*sinθ1 and Τ1*sinθ2 Their sum is equal to 350 N.
Horizontal components are T1*cosθ1 and Τ1*cosθ2 and they are equal. As I have told you, you have two equations. Solve them to find T1 and T2.
 

1. How do you determine the tension in cement bag wires?

To determine the tension in cement bag wires, you must first calculate the weight of the cement bag and its contents. Then, using the length and diameter of the wire, you can calculate the cross-sectional area and use this to determine the stress on the wire. Finally, using Hooke's Law, the tension can be calculated by dividing the stress by the cross-sectional area.

2. What factors affect the tension in cement bag wires?

The tension in cement bag wires can be affected by several factors, including the weight and size of the cement bag, the type and strength of the wire, and the environment in which the bag is stored. Other factors such as handling and transportation can also impact the tension in the wires.

3. How can you ensure the correct tension in cement bag wires?

To ensure the correct tension in cement bag wires, it is important to use high-quality wires that are designed for this purpose. Proper handling and storage of the cement bag can also help maintain the tension in the wires. Regular inspections and adjustments may be necessary to ensure the tension remains at the desired level.

4. What are the consequences of incorrect tension in cement bag wires?

Incorrect tension in cement bag wires can lead to various issues, such as the bag breaking or tearing during handling or transportation, which can result in spillage and damage to the contents. It can also affect the stability of the bag, causing it to shift or collapse. In extreme cases, incorrect tension can cause the wires to snap, potentially causing injuries to workers.

5. Can the tension in cement bag wires be adjusted after the bag is filled?

In most cases, the tension in cement bag wires cannot be adjusted after the bag is filled. It is crucial to ensure the correct tension is applied before filling the bag to avoid any issues. However, in some cases, slight adjustments may be possible by manually tightening or loosening the wires, but this should be done with caution to avoid damaging the bag or its contents.

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