Standard +0.3 This is a standard two-stage pulley problem requiring Newton's second law for connected particles, then projectile motion after string goes slack. Part (i) is a 'show that' with straightforward application of F=ma to the system. Parts (ii-iii) are routine bookwork. Part (iv) requires finding velocity when Q hits ground, then using kinematic equations for upward motion—all standard techniques with no novel insight needed. Slightly above average due to the two-stage nature and multiple parts, but well within typical A-level mechanics scope.
5. Two particles \(P\) and \(Q\) have masses 2 kg and 5 kg respectively. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially both \(P\) and \(Q\) are 2.1 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{6c69f370-0d2d-41ec-8761-0707a6ada43d-10_417_182_358_1032}
i. Show that the acceleration of \(Q\) as it descends is: \(4.2 \mathrm {~ms} ^ { - 2 }\)
ii. Find the tension in the string as \(Q\) descends.
iii. Explain how you have used the information that the string is inextensible and that the pulley is smooth.
When \(Q\) hits the ground it does not rebound and the string becomes slack. Particle \(P\) then moves freely under gravity without reaching the pulley.
iv. Find the greatest height above the ground that \(P\) reaches. [0pt]
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5. Two particles $P$ and $Q$ have masses 2 kg and 5 kg respectively. The particles are connected by a light inextensible string which passes over a smooth, fixed pulley. Initially both $P$ and $Q$ are 2.1 m above horizontal ground. The particles are released from rest with the string taut and the hanging parts of the string vertical, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{6c69f370-0d2d-41ec-8761-0707a6ada43d-10_417_182_358_1032}\\
i. Show that the acceleration of $Q$ as it descends is: $4.2 \mathrm {~ms} ^ { - 2 }$\\
ii. Find the tension in the string as $Q$ descends.\\
iii. Explain how you have used the information that the string is inextensible and that the pulley is smooth.
When $Q$ hits the ground it does not rebound and the string becomes slack. Particle $P$ then moves freely under gravity without reaching the pulley.\\
iv. Find the greatest height above the ground that $P$ reaches.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Mechanics 2021 Q5 [13]}}