A tether ball of mass 0.25 kg is attached to a vertical pole by a cord 1.4 m long. Assume the cord attaches to the center of the ball. The cord makes an angle of 20° with the vertical.

Question

(a) What is the tension in the cord?

(b) What is the speed of the ball?

Answer 1

r = radius of circle = 1.4 sin 20
centripetal acceleration = v^2/r
horizontal force needed = m v^2/r
but
horizontal component of tension = T sin 20
vertical component of tension = T cos 20 = m g
so
T = m g/cos 20 = 2.61 Newtons (part A)

so
T sin 20 = m v^2/r = m v^2/1.4 sin 20
2.61 (1.4 )sin^2 20 = .25 v^2
solve for v