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## Homework Statement

A 100 g bead is free to slide along an 80 cm long piece

of string ABC. The ends of the string are attached to a

vertical pole at A (bottom) and C (top), which are 40 cm apart. When

the pole is rotated about its axis, AB becomes

horizontal.

a. Find the tension in the string.

b. Find the speed of the bead at B.

## Homework Equations

a

^{2}+b

^{2}=c

^{2}

F

_{R}= mv

^{2}/r

## The Attempt at a Solution

Using pythagoras I figured out that the radius (AB) is .3m

Using sinθ (.4/.5) the angle at B is 53.1 degrees

Using a FBD, it appears that the bead has 2 forces acting on it in a vertical direction: mg and a force upwards ("Fc") from the BC string segment. The vertical component of this force must equal mg because there is no acceleration in the y direction (or, at least that's my logic).

So: Fc sin 53.1 = mg

Fc vertical = (.1)(9.8)/sin 53.1 = 1.23

This is where I come to problems. For the horizontal component, it seems like Fnet would equal the centripital force pulling inwards towards A plus the horizontal component of the force from BC string. Would the equation be Fc(cosθ) = mv

^{2}/r? How would I solve this without knowing Fc horizontal or velocity? I don't even know if I am on the right track, I feel so confused Any advice?