A mass is attached to two strings, derive a formulas for sum of forces

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Homework Help Overview

The problem involves a 300 g sphere attached to two wires, revolving in a horizontal circle at a constant speed of 6.50 m/s. The discussion centers on deriving formulas for the sum of forces acting on the sphere, particularly focusing on the tensions in the upper and lower wires and their relationship.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to formulate equations for the sum of forces along the vertical and horizontal axes, questioning how to demonstrate that the tension in the upper wire (T2) is greater than that in the lower wire (T1).
  • Some participants inquire about the visual representation of the problem to better understand the setup.
  • One participant suggests using the relationship between the tensions and gravitational force to establish the inequality between T2 and T1.
  • Another participant proposes using centripetal force considerations to relate the tensions to the motion of the sphere.

Discussion Status

The discussion is active, with participants exploring different aspects of the problem. Some guidance has been offered regarding the relationships between the forces and the use of equations, but there is no explicit consensus on the approach to take.

Contextual Notes

The original poster expresses uncertainty about how to start the problem and the need for clarification on the relationships between the forces involved. The discussion also references a figure that is crucial for understanding the problem setup.

Kat11111
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Homework Statement


Two wires are tied to the 300 g sphere shown in figure. The sphere revolves in a horizontal circle at a constant speed of 6.50 m/s. What is the tension in the upper wire?What is the tension in the lower wire? Write an equation for the sum of the forces along y. Use it to show that T2 is bigger than T1. Then, write sum of the forces along x.



Homework Equations


ac=v^2\r
sin(theta)t2-sin(theta)t1=mg


The Attempt at a Solution



I didn't know where to start for the first two questions and for the last one, I came up with the sin(theta)T2-sin(theta)t1=mg but I didn't know how to prove that T2 is bigger than T1. Could you please help me?
 
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What does the figure look like-- do you have a picture?
 
We know that if A = B1 + B2 + B3 +... and A, Bn are positive, we can conclude that A > Bn

You have T2*sin(theta) = T1*sin(theta) + mg. Because all values in this eq are positive. Therefore, T2*sin(theta) > T1*sin(theta) => T2 > T1

In X-axis, you should use centripetal force: (T2 + T1)*cos(theta) = mv^2/R and use above eq that you use to show that T2 > T1 to find values of these forces.
 

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