Answer Happy

L1. A particle with mass m is attached to one end of an inextensible string of length l. The other end of the string is attached at point O vertically above the particle. The particle is then struck to move on a vertical circle of radius l with initial horizontal speed u. (a) Show that when the string makes an angle with the downward vertical, the tension in the string is u2 T = m + mg(3 cos 0 – 2). ) [7 marks] (b) Show that the particle will describe at least a half-circle provided u> V5gl. [3 marks) = (c) The particle is given an initial horizontal speed u = Vgl. Compute (to the nearest degree) the angle at which the string flexes. [3 marks] (d) Also when the particle is given an initial horizontal speed u = vgl, compute (u (to the nearest degree) the angle at which it comes to rest instantaneously while on the vertical circular motion, and thus find which event occurs first. [3 marks] (e) When the particle is oscillating back and forth with T > 0 at all times, what is the exact equation for e(t) describing the motion? What is the approximate equation for small oscillations? (4 marks]