Question

An inextensible massless string of length 2l has mass mand m3 attached to the two ends A and B respectively. A particle of mass m2 is attached to the midpoint of the string at point C. Initially, the three particles are at the vertices of an equilateral triangle as shown in the figure below and the string is taut. Particle 2 is given an impulse J along the bisector of the angle ACB. It is known that the whole set up is on a smooth surface. 7m 7m 7m 3 (a) In the particular case ml = m3 = m and m2 = 3m, calculate in terms of/ the velocity of the three particles when particles 1 and 3 begin to move. (b) Consider the general case for any arbitrary mass mi, m2 and m3. Show that at the moment when the string is taut again and particles 1 and 3 begin to move, the angle θ between the direction of motion of particle 2 and the x-axis is given by: m1 + 4m2+m3

Answer 1

3 2 rm 1 5m m-2