Question

A 0.50 kg ball that is tied to theend of a 1.0 m light cord is revolvedin a horizontal plane with the cord making a 30° angle, withthe vertical (See Fig. P7.52.)

Figure P7.52

(a) Determine the ball's speed.
m/s
(b) If, instead, the ball is revolved so that its speed is 4.0 m/s,what angle does the cord make with the vertical?
°
(c) If the cord can withstand a maximum tension of 9.1 N, what is the highest speed at which the ballcan move?
m/s

Answer 1

(a)Ball's mass, m = 0.50 KgLength of the cord is, L = 1.0 mAngle of inclination, θ =30°Now to deflect the cord through an angleθ from the vertical we need force,
F = M g TanθThis force should be supplied by thecentripetal force, F = M V² / RM g Tanθ= M V² /RWhere, R = L sinθ
From this get the value of V(b)Speed of the ball is, V = 4.0m/sTanθ = V² /RgWhere, R = L sinθPlug the values in the above expression andget the answer(c)Horizontal component of the tension in thestring provides necessary centripetal forceT sinθ = M v² /RWhere, R = L sinθPlug the vlaues and get the value of thetension in the string