For the mechanism shown , with the ball revolving with 5 m radius , find the velocity of the ball and the tension in the cord. The length of the cord is 10 m , while the mass of the ball is 2 kg. The unstretched length of the spring is 4 m and the spring stiffness is k = 10 N/m.

1) T = 61.15 N, v = 7.49 m/s2

2) T = 21.24 N, v = 1.24 m/s2.
3) T = 45.45 N, v = 4.56 m/s2.
4) T = 68.23 N, v = 5.76 m/s2.

sin f = R/L = 5/10 =0.5.
f
= 30o.

(AO)2 = (AL)2 -(R)2.
= 8.66 m.

Height of ball from base = 15 - 8.66 = 6.34 m.
cos(90o - q) = R/H = 5/6.34 = 0.788 m.
q = 90o - 37.54 = 52.46o.
Length of the stretched spring = R/cos q = 8.205 m.
Fs = kx = 10(4.205) = 42.05 N.

The equations of motion for the ball are as follows-
Tcos 30 - 42.05 sin 52.46 - 2(9.81) = 0. -----------(1)
T sin 30 + 42.05 cos 52.46 -2(v)2/2 = 0 ----------(2)

This gives T = 61.15 N.
v = 7.49 m/s2.