Challenging +1.2 This is a multi-stage pulley problem requiring students to: (1) find Q's mass using tension equation, (2) calculate Q's velocity when P hits ground using energy or kinematics, (3) determine additional height Q rises after string goes slack, and (4) calculate total distance (up then down). While it involves several connected steps and careful tracking of motion phases, each individual calculation uses standard M1 techniques (Newton's laws, SUVAT, energy). The conceptual demand is moderate—understanding that Q continues upward after P stops is a key insight but fairly standard for pulley problems.
3 Particles \(P\) and \(Q\) are attached to opposite ends of a light inextensible string which passes over a fixed smooth pulley. The system is released from rest with the string taut, with its straight parts vertical, and with both particles at a height of 2 m above horizontal ground. \(P\) moves vertically downwards and does not rebound when it hits the ground. At the instant that \(P\) hits the ground, \(Q\) is at the point \(X\), from where it continues to move vertically upwards without reaching the pulley. Given that \(P\) has mass 0.9 kg and that the tension in the string is 7.2 N while \(P\) is moving, find the total distance travelled by \(Q\) from the instant it first reaches \(X\) until it returns to \(X\).
3 Particles $P$ and $Q$ are attached to opposite ends of a light inextensible string which passes over a fixed smooth pulley. The system is released from rest with the string taut, with its straight parts vertical, and with both particles at a height of 2 m above horizontal ground. $P$ moves vertically downwards and does not rebound when it hits the ground. At the instant that $P$ hits the ground, $Q$ is at the point $X$, from where it continues to move vertically upwards without reaching the pulley. Given that $P$ has mass 0.9 kg and that the tension in the string is 7.2 N while $P$ is moving, find the total distance travelled by $Q$ from the instant it first reaches $X$ until it returns to $X$.
\hfill \mbox{\textit{CAIE M1 2011 Q3 [6]}}