can i have some help please?
A particle, of mass 8kg, is attached to one end of a length of elastic string. The particle is placed on a smooth horizontal surface. The other end of the elastic string is attached to a point O fixed on the horizontal surface.
The elastic string had natural length 1.2m and modulus of elasticity 192N.
The particle is set in motion on the horizontal surface so that it moves in a circle, centre O, with a constant speed 3m/s.
Find the radius of the circle.
ive used t=(mv^2)/r where t is the centripetal force
i thought that this might be equal to the string when its moving so i set it equal to ?x/l
?=192, l=1.2 x(the extension) = r-l?
(mv^2)/r = ?x/l
8x9/r = 192(r-1.2)/1.2
0.45=r(r-1.2)
r^2 -1.2r -0.45=0
i've ended up with a quadratic which i solved and selected the positive solution
my final answer for the radius is 1.5m can anyone confirm?