Estimate the force a person must exert on a string.?

Estimate the force a person must exert on a string attached to a 0.175 kg ball to make the ball revolve in a horizontal circle. The ball makes 2.40 revolutions per second (T = 0.417 s ). Don't ignore the weight of the ball which revolves on a string 0.630 m long. In particular, find the magnitude of F⃗ T. [Hint: Set the horizontal component of F⃗ T equal to maR; also, since there is no vertical motion, what can you say about the vertical component of F⃗ T?]. Find the angle F⃗ T makes with the horizontal. Someone, please help me with this because I'm lost.

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  • NCS
    Lv 7
    4 weeks ago

    The geometry of the string gives the geometry of the forces:

    tanΘ = Fc / Fg = mω²r / mg = ω²r / g

    where Θ is the angle the string makes with vertical.

    ω = 2π/T = 2π / (1s / 2.40) = 15.08 rad/s

    but also

    tanΘ = opp/adj = r / √(L² - r²)

    so

    r / √(L² - r²) = ω²r / g

    √(L² - r²) = g / ω²

    Plug in L = 0.630 m

    g = 9.81 m/s²

    ω = 15.08 rad/s

    and solve; I get

    r = 0.629 m

    Fc = mω²r = 0.175kg * (15.08rad/s)² * 0.629m = 25.0 N

    Fg = mg = 0.175kg * 9.81m/s² = 1.72 N

    tension T = √(Fc² + Fg²) = 25.1 N

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