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

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    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.



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


    3. 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?
     
  2. jcsd
  3. Nov 2, 2009 #2
    What does the figure look like-- do you have a picture?
     
  4. Nov 2, 2009 #3
  5. Nov 2, 2009 #4
    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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