June 2025 Paper 3 Q8
8
Two particles \(A\) and \(B\) of masses 0.6 kg and 0.8 kg respectively, are attached to the ends of a light inextensible string. Particle \(A\) is held at rest at a fixed point and \(B\) hangs vertically below \(A\).
Particle \(A\) is now released. As the particles fall the air resistance acting on \(A\) has a constant magnitude of \(R\) N and the air resistance acting on \(B\) has a constant magnitude of 0.3 N. The string remains taut throughout the subsequent motion (see diagram).
The downward acceleration of each of the particles is 9.2 m s−2 and the tension in the string is \(T\) N.
| Scheme | Marks | AO |
|---|---|---|
| \(0.8g - 0.3 - T = 0.8(9.2)\) | M1 | 3.3 |
| \(T = 0.18\) | A1 | 1.1 |
| [2] |
Notes
M1: Applying N2L for \(B\) with correct number of dimensionally correct terms (so allow sign errors only) to obtain an equation in \(T\) only
This mark is not awarded until all values have been correct substituted into N2L so, for example, must see 0.8 for the mass (and not just \(m\))
A1: cao – must be positive oe e.g. \(\frac{9}{50}\)
| Scheme | Marks | AO |
|---|---|---|
| \(0.6g + T - R = 0.6(9.2)\) | M1 | 3.3 |
| \(R = 0.54\) | A1 | 1.1 |
| [2] |
Notes
M1: Applying N2L for \(A\) with correct number of dimensionally correct terms (so allow sign errors only) to obtain an equation in \(R\) (and possibly \(T\)) only. Alternative is to consider N2L for the system which if correct is \(0.8g - 0.3 + 0.6g - R = 1.4(9.2)\) (if considering this equation then allow sign errors only)
Allow the letter \(T\) or their (possibly incorrect) value of \(T\)
A1: cao – must be positive oe e.g. \(\frac{27}{50}\)