Minimizing Tension: Solving for Unknown Angle in Hanging Package Problem

Then, use the equations to solve for the unknown angle of cord two and the minimum tension in cord 2.In summary, to find the minimum tension in cord 2, you must draw a free-body diagram for the hanging mass and use Newton's second law to solve for the unknown angle and minimum tension.
  • #1
mdoucette225
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Homework Statement


A package of mass m hangs from a short chord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at an angle 40 degrees with the horizontal cord two is at an unknown angle.
-For what value of the unknown angle of cord two is the tension minimized?
-In terms of mg, what is the minimum tension in cord 2?


Homework Equations





The Attempt at a Solution


mg= FT1 +FT2. I attempted to find the minimum tension first, but honestly I have no idea where to start
 
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  • #2
First, draw a free-body diagram for every mass. Draw out all forces and write down Newton's second law for both the x and the y components.
 

Related to Minimizing Tension: Solving for Unknown Angle in Hanging Package Problem

What is the purpose of minimizing tension in a hanging package problem?

The purpose of minimizing tension is to ensure that the hanging package is stable and does not fall due to excessive force or weight. This is important for both safety reasons and to prevent damage to the package and its contents.

What factors affect the tension in a hanging package?

The tension in a hanging package is affected by the weight of the package, the angle at which it is hung, and the strength and length of the rope or string holding it.

How can the unknown angle in a hanging package problem be solved?

The unknown angle in a hanging package problem can be solved using trigonometric equations and principles such as the sine, cosine, and tangent functions. The weight of the package and the tension in the rope can also be used to determine the angle.

What are some common methods for minimizing tension in a hanging package problem?

Some common methods for minimizing tension include using a shorter rope or string, distributing the weight of the package evenly, and adjusting the angle at which the package is hung.

Why is it important to minimize tension in a hanging package problem?

Minimizing tension is important to ensure the stability and safety of the hanging package. Excessive tension can cause the package to fall and potentially cause injury or damage. It also helps to prolong the lifespan of the rope or string used to hang the package.

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