Question

6) In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at point O. The ball is held at point A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters ofa circle with no friction and arrives at B, with the rope barely under tension. 1 11.6 m 4.0 kg A Vo (a) Write out the expression for the sum of the forces in the radial direction? (b) Write a formula for the tension in the cord at any angle: (c) What is the tension at point B? (d) What is the initial velocity of the ball when released from point A so that the tension at point B is zero?

Answer 1

a] Forces in radial direction, F = mv^2/r

b] T - mg*sin theta = mv^2/r where theta is angle with OA,

c] T = 0 as the rope is not in tension

d] Let initial velocity be u,

Let velocity at top be v , mv^2/r = mg , or  0.5mv^2 = 0.5mgr

by energy conservation, 0.5mu^2 = mgr + 0.5mgr

u = sqrt(3rg)