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newtophysics2
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Homework Statement
A ball of mass m is attached by two strings to a vertical rod. as shown in the diagram attached. The entire system rotates at constant angular velocity ω about the axis of the rod.
a)Assuming ω is large enough to keep both strings taut, find the force each string exerts on the ball in terms of ω, m, g, R, and θ.
b)Find the minimum angular velocity, θ_min for which the lower string barely remains taut.
Homework Equations
F_centripetal=mv2/r
F=ma
The Attempt at a Solution
A) To keep the strings taut, the net force in the y-axis and the x-axis have to both equal 0. I used forces and tension, but my answer didn't contain ω, but I feel like it should...
T1 tension is making θ angle with the vertical
T1cosθ along vertical upward
T1sinθ along horizental i.e towards the center of the circular path
applying ΣFy =0 ΣFx =0
T1cosθ=mg
T1=mg/cosθ
T1sinθ+T2=mv2/R
T2=mgsinθ+mv2/R
B) I would solve for v from the equations above, but the question doesn't say that I can use T (tension) in my answer...
What am I doing wrong in this problem? Thanks in advance!