Question:
A particle P of mass 2.5kg is attached to fixed points A and B by light inextensible strings, each of length 50cm. A and B are 96cm apart with A vertically above B. Particle P moves in a horizontal circle with centre at thr midpoint of AB. Find the least possible speed of P.
Given Answer:
$32.6ms^{-1}$
My Attempt:
1. Derive relationship between T_1 and T_2 by resolving the forces vertically. Result: $T_1 = T_2 + \frac{625}{24}$
2. Assuming that the least possible speed means the minimum speed while the two strings remain taunt. Therefore it occurs when $T_2 = 0$, consequently $T_1 = \frac{625}{24}$.
3. Resolve horizontally for an equation linking centripetal force and T_1. $\frac{0.14 * T_1}{0.50} = F_c = \frac{2.5 * v^2}{0.14}$
3. Solve for $v$.
4. $v = 0.639$