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Tension in the String

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data

    "What is the tension in the string?"

    • .5kg block
    • Suspended at the midpoint of a 1.25m-long string
    • Ends of string attached to ceiling are 1m apart.


    2. Relevant equations

    cosθ, sinθ, tanθ

    T[itex]_1[/itex][itex]_x[/itex]+T[itex]_2[/itex][itex]_x[/itex]+F[itex]_g[/itex][itex]_x[/itex]=ma[itex]_x[/itex]

    T[itex]_1[/itex][itex]_y[/itex]+T[itex]_2[/itex][itex]_y[/itex]+F[itex]_g[/itex][itex]_y[/itex] = T[itex]_1[/itex][itex]_y[/itex]+T[itex]_2[/itex][itex]_y[/itex]- F[itex]_g[/itex] = ma[itex]_x[/itex]


    3. The attempt at a solution

    My homework is online and immediately verifies whether or not your answers are correct. I was able to solve that the angle the string makes with the ceiling is 36.87°.

    From there, I attempted to solve for T[itex]_1[/itex] and T[itex]_2[/itex] as follows:

    T[itex]_1[/itex][itex]_x[/itex]+T[itex]_2[/itex][itex]_x[/itex]+F[itex]_g[/itex][itex]_x[/itex]=ma[itex]_x[/itex].

    ⇔ T[itex]_1[/itex]cos(36.87°) - T[itex]_2[/itex]cos(36.87°) + 0 = 0 (since the force of gravity has no affect on the x-component of the tensions, and the object is not accelerating).

    ⇔ T[itex]_2[/itex] = T[itex]_1[/itex]cos(36.87°)/cos(36.87°) = T[itex]_1[/itex].

    T[itex]_1[/itex][itex]_y[/itex]+T[itex]_2[/itex][itex]_y[/itex]+F[itex]_g[/itex][itex]_y[/itex]=0.

    ⇔ T[itex]_1[/itex]sin(36.87°) +T[itex]_2[/itex]sin(36.87°)=F[itex]_g[/itex]

    ⇔ 2T[itex]_1[/itex]sin(36.87°)=F[itex]_g[/itex]

    Therefore,

    ⇔ T[itex]_1[/itex]=.5kg(9.8m/(s2))/(2*sin(36.87°)) = 4.083N.

    I've used up all but one of my attempts. Maybe it's because I'm not understanding the wording of the problem. I used up two attempts by guessing T[itex]_1[/itex]+T[itex]_2[/itex] = 8.16/8.17 (I thought that it may be an issue with rounding).

    Anyway, if someone could provide some input as to what the problem is asking, I would be extremely appreciative! And it would also be nice to have someone verify that my math and setup of this problem is correct. Thank you so much!
     
    Last edited: Oct 9, 2012
  2. jcsd
  3. Oct 9, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    I think you just miss a zero. It is 4.083 N

    ehild
     
  4. Oct 9, 2012 #3
    Whoops, I think I actually did use 4.083 when I submitted my answer. Later in my post you see that I said that T[itex]_1[/itex]+T[itex]_2[/itex] equals 8.16/8.17, which is double 4.08.

    Editing first post to reflect that.
     
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