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

AI Thread Summary
The discussion focuses on deriving formulas for the tensions in two wires attached to a 300 g sphere revolving in a horizontal circle at 6.50 m/s. The equation for the sum of forces in the vertical direction is established as T2*sin(theta) - T1*sin(theta) = mg, demonstrating that T2 is greater than T1 due to the positive nature of all terms. For the horizontal forces, the centripetal force equation (T2 + T1)*cos(theta) = mv^2/R is suggested to find the values of the tensions. The relationship between the tensions is confirmed through the derived equations. The discussion emphasizes the importance of understanding the forces acting on the sphere to solve for the tensions accurately.
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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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