Question

A 5.65-kg ball hangs from the top of a vertical pole by a 2.05-m-long string. The ball is struck, causing it to revolve around the pole at a speed of 4.13 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0

Answer 1

r = L*sintheta

Tsintheta = mv^2/r = mv^2/Lsintheta

(T*sin theta)^2 = mv^2/L..............(1)

Tcostheta = mg

(T*costheta)^2 = m^2*g^2..............(2)

1/2

tantheta^2 =v^2/mLg^2 = (4.13^2)/(5.65*2.05*9.81^2)

theta = 7.05

Answer 2

by conservation of energy

mgl(1 - cos $\theta$ ) = 1/2mv^2

substituting values in above equation

cos $\theta$ = 0.576

$\theta$ = 54.83 degrees