Question

a) Tetherball is a game that uses a ball hanging from a string attached to the top of a post, where the ball is sent flying around in the tangential direction. Assume a uniform gravitational acceleration g pointed downward. This is an example of what is known as a “conical pendulum.”

i) Find the equilibrium angle that the string makes with the vertical for a given speed v such that the ball traces a circle at uniform height.

ii) Estimate the angular frequency for the motion, and then take the limit where the speed is very small. You should recognize something.

b) A massive block is placed on top of a very slippery sphere and given an initial speed v◦ in a horizontal direction. Find the angle at which the block loses contact with the sphere. Assume a uniform gravitational acceleration g pointed downward.

Answer 1

(1) af equilibrium Tsino = mva ti TL force and T Como = mg, euismod and I load from c) and (ii) tano - e -Cill) eqn Child 22 rgtano => VzSoglaning but since way gtano

hae It ball leave? Cblack) the Abhere at @che the velocity of the ball v after moving height hl vzvo? +29h 2) v = 26 27 29h (1) from fig (ti) mg como - maes o where acs uz now from (i) and (ii) CORO = 12 r. 2+29h from figci) Cone = Roh => Vo? = RJ – 3gh => h3>

now putting above value of h in eqh (3) we get Cone = te noe +29 (-762+ R9) Rg >> - Can' (1 te))
if you have any doubts, feel free to ask.