A bob of mass = 0.250 is suspended from a fixed point with a massless string of length = 23.0 . You will investigate the motion in which the string traces a conical surface with half-angle = 25.0.

Question

What tangential speed must the bob have so that it moves in a horizontal circle with the string making an angle 25.0 with the vertical?

Im setting it up right but keep getting the wrong answer

Answer 1

The radius of the circle comes from trig:

radius=length*tangent25=23*tan25

but centripetal acceleration must equal the force of gravity pushing the bob inward, so

v^2/r=g*sin25

solve for v.