Moderate -0.8 This is a straightforward two-particle connected system problem requiring application of Newton's second law to each mass separately. The setup is standard (vertical arrangement, constant force), and the solution involves writing two equations (F=ma for each particle) and solving simultaneously for acceleration and tension. It's easier than average as it requires only routine application of a well-practiced technique with no geometric complexity or novel insight.
Two particles \(P\) and \(Q\), of masses 0.5 kg and 0.3 kg respectively, are connected by a light inextensible string. The string is taut and \(P\) is vertically above \(Q\). A force of magnitude 10 N is applied to \(P\) vertically upwards.
Find the acceleration of the particles and the tension in the string connecting them. [5]
For P: 10 – 0.5g – T = 0.5a, For Q: T – 0.3g = 0.3a,
Answer
Marks
Guidance
For system: 10 – 0.5g – 0.3g = 0.8a
A1
For any two correct
For attempt to solve for either a or T
M1
From equation(s) with no missing or extra terms. Allow g missing.
a = 2.5 ms–2
A1
T = 3.75 N
A1
5
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Use of Newton’s second law for P or Q or system | M1 | Allow sign errors. Do not allow g missing
For P: 10 – 0.5g – T = 0.5a, For Q: T – 0.3g = 0.3a,
For system: 10 – 0.5g – 0.3g = 0.8a | A1 | For any two correct
For attempt to solve for either a or T | M1 | From equation(s) with no missing or extra terms. Allow g missing.
a = 2.5 ms–2 | A1
T = 3.75 N | A1
5
Question | Answer | Marks | Guidance
Two particles $P$ and $Q$, of masses 0.5 kg and 0.3 kg respectively, are connected by a light inextensible string. The string is taut and $P$ is vertically above $Q$. A force of magnitude 10 N is applied to $P$ vertically upwards.
Find the acceleration of the particles and the tension in the string connecting them. [5]
\hfill \mbox{\textit{CAIE M1 2022 Q2 [5]}}