October 2020 Paper 1 Q11
11 A block of mass 2 kg is placed on a rough horizontal table. A light inextensible string attached to the block passes over a smooth pulley attached to the edge of the table. The other end of the string is attached to a sphere of mass 0.8 kg which hangs freely.
The part of the string between the block and the pulley is horizontal. The coefficient of friction between the table and the block is 0.35. The system is released from rest.
| Scheme | Marks | AO |
|---|---|---|
 | B1 B1 B1 | 1.1a 1.1a 1.1a |
| [3] |
Notes
B1: both weights correct.
B1: common tension in the rigtht directions
B1: Friction and normal reaction and no extra forces
Allow weight of box and weight of sphere, but not if both marked weight.
Allow \(T_1\) and \(T_2\) provided they are clearly shown equal to each other elsewhere.
For \(F\), allow \(0.35R,\ 0.35 \times 2g\) \(0.7g\) or 6.86 N
| Scheme | Marks | AO |
|---|---|---|
| \(T - F = 2a\) | B1 | 1.1a |
| \(0.8g - T = 0.8a\) | B1 | 1.1a |
| [2] |
Notes
B1: Allow any expression for F
B1: Allow distinct tensions if consistent with diagram
For \(F\), allow \(0.35R,\ 0.35 \times 2g\) \(0.7g\) or 6.86 N
| Scheme | Marks | AO |
|---|---|---|
| Vertically for the block \(R = 2g\) | M1 | 3.1b |
| Friction \(F = 0.35R = 0.7g\) | A1 | 2.1 |
| Add equations \(0.8g - F = 2.8a\) | M1 | 2.1 |
| \(0.8g - 0.7g = 2.8a\) \(a = 0.35\,\mathrm{m\,s^{-2}}\) | A1 | 2.1 |
| [4] |
Notes
M1: Attempt to use \(\mu\) to evaluate friction
A1: Correct value for F
M1: Eliminate \(T\) from their equations
A1: AG must follow from correct work
Some of this work may already have been seen in previous part
| Scheme | Marks | AO |
|---|---|---|
| Use \(s = 0.5,\quad u = 0,\quad a = 0.35\) \(0.5 = \dfrac{1}{2} \times 0.35 \times t^2\) | M1 | 1.1a |
| \(t = 1.69\) s | A1 | 1.1 |
| [2] |
Notes
M1: Using suvat equation(s) leading to a value for \(t\)
A1: Do not allow \(\pm 1.69\)