A 1.13 kg ball is connected by means of two ideal strings to a vertical, rotating rod. The strings are tied to the rod and are taut. The upper string is 24.0 cm long and has a tension of 31.5 N, and it makes an angle θ2 = 51.0° with the rod, while the lower string makes an angle θ1 = 55.0° with the rod. (a) What is the tension in the lower string? (b) What is the speed of the ball?

Question

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Answer 1

look at each string tension ...
tensionin1=31.5 cos51
tensionvertical1=31.5sin51

but the tension vertical in the lower string must be equal to the upper vertical tension..
tensionvertica2=Tensionlower*cos55
31.5sin51=Tensionlower*cos55
solve for tension in the lower string.

Now, the inward portion of that tension is
tensionlowerSin55

now add the two inward components of tension, and set them equal to centripetal force.
tensionin1+tensionin2=mv^2/r
where r is 24sin51 solve for v.