Question

A student is swinging a ball on a string overhead in a horizontal plane. The string initially has length ?0 and the ball is moving with an initial speed ?0. The student decides to see how fast they can spin the ball, so they begin moving it faster and faster with a constant tangential acceleration ?? . However, they know that the string is close to breaking, so they decide to keep letting the string get longer and longer in order to keep the tension in the string constant. Find expressions for the length of the string and the total acceleration (magnitude and direction) as a function of time, ?0, ?0, and ?? . You may ignore the effect of gravity on the ball.

Answer 1

We have + Hur me ato tangential acci VA) speed of lime t. a integrating on both sides. V(t)= Vot ap 0. Now tension in the string. TO mv() 1 ) Silt Tension romains Coves fant! T(0) = mv * mwayan meme >> lce) veemplo or using oqm (1) - Telo lo (vot act) | Now tolal acceleration is given as mora r Chere ac is cant contripetal acceleration). Nee VCC)? e) Vo+04+)2V,2 7 5? e ( l (Vo-tart To Acceleration & ato - V² F Magnitude = Vap² + (me) ² Dinceton =