Moderate -0.8 This is a standard two-particle pulley system with straightforward application of Newton's second law to both particles. Students need to write F=ma for each mass, recognize that tensions are equal and accelerations have the same magnitude, then solve two simultaneous equations. It's a routine textbook exercise requiring only basic mechanics principles with no problem-solving insight or geometric complications.
1
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Two particles \(P\) and \(Q\), of masses 0.6 kg and 0.4 kg respectively, are connected by a light inextensible string. The string passes over a small smooth light pulley fixed at the edge of a smooth horizontal table. Initially \(P\) is held at rest on the table and \(Q\) hangs vertically (see diagram). \(P\) is then released. Find the tension in the string and the acceleration of \(Q\).
\(0.4g - T = 0.4a\) and \(T = 0.6a\), System equation: \(0.4g = (0.4 + 0.6)a\)
M1
For applying Newton's 2nd law to either particle or to the system
(Second equation and attempt to solve for \(a\) and \(T\))
M1
For applying Newton's 2nd law to the other particle and attempt to solve for \(a\) and \(T\)
\(a = 4\text{ ms}^{-2}\)
A1
\(T = 2.4\text{ N}\)
A1
[4]
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $0.4g - T = 0.4a$ and $T = 0.6a$, System equation: $0.4g = (0.4 + 0.6)a$ | M1 | For applying Newton's 2nd law to either particle or to the system |
| (Second equation and attempt to solve for $a$ and $T$) | M1 | For applying Newton's 2nd law to the other particle and attempt to solve for $a$ and $T$ |
| $a = 4\text{ ms}^{-2}$ | A1 | |
| $T = 2.4\text{ N}$ | A1 | [4] |
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\includegraphics[max width=\textwidth, alt={}, center]{a92f97e2-343f-4cac-ae38-f18a4ad49055-2_241_823_264_660}
Two particles $P$ and $Q$, of masses 0.6 kg and 0.4 kg respectively, are connected by a light inextensible string. The string passes over a small smooth light pulley fixed at the edge of a smooth horizontal table. Initially $P$ is held at rest on the table and $Q$ hangs vertically (see diagram). $P$ is then released. Find the tension in the string and the acceleration of $Q$.
\hfill \mbox{\textit{CAIE M1 2016 Q1 [4]}}