June 2024 Paper 3 Mechanics Q1
1.
Figure 1 shows a particle \(P\) of mass 0.5 kg at rest on a rough horizontal plane.
The coefficient of friction between \(P\) and the plane is \(\dfrac{2}{7}\)
A horizontal force of magnitude \(X\) newtons is applied to \(P\).
Given that \(P\) is now in limiting equilibrium,
| Scheme | Marks | AO |
|---|---|---|
| \(0.5g,\ \dfrac{1}{2}g\) or \(4.9\) (N) seen | B1 | 3.4 |
| (1) |
Notes
Ignore units in this question.
N.B. Use of \(g = 9.81\) should only be penalised once for the whole question as should two fractional answers (a) 49/10 (b) 7/5.
Penalise the use of \(g = 9.81\) the first time you see it.
N.B.
If \(g = 9.81\) is used in (a), B0. If it is then used again in part (b), and they give the answer as 1.4 or 1.40, they can score M1A1 in part (b).
If \(g = 9.81\) is only used in (b), they can score max M1A0 for (b).
B1: cao. (must be positive)
B0 for a fraction \(\left(\dfrac{49}{10}\right)\)
B0 if they have \(0.5g\) and then clearly use \(g = 9.81\) i.e. NOT isw
This answer must appear in (a) to earn this mark. If no labelling, give BOD and award as many marks as possible.
| Scheme | Marks | AO |
|---|---|---|
| \(\dfrac{2}{7} \times 4.9\) oe seen | M1 | 3.1a |
| 1.4, 1.40 or \(\frac{1}{7}g\) | A1 | 1.1b |
| (2) | ||
| (3 marks) |
Notes
Ignore units in this question.
N.B. Use of \(g = 9.81\) should only be penalised once for the whole question as should two fractional answers (a) 49/10 (b) 7/5.
Penalise the use of \(g = 9.81\) the first time you see it.
N.B.
If \(g = 9.81\) is used in (a), B0. If it is then used again in part (b), and they give the answer as 1.4 or 1.40, they can score M1A1 in part (b).
If \(g = 9.81\) is only used in (b), they can score max M1A0 for (b).
M1: \(\dfrac{2}{7} \times\) their (a) (must be a numerical value)
If no answer for (a) or if (a) is incorrect and they don’t use it, allow a correct restart i.e.
\(\dfrac{2}{7} \times 4.9\) or \(\dfrac{2}{7} \times 0.5g\) or \(\dfrac{2}{7} \times 0.5\) (missing \(g\) is not an M error)
A1: A0 for a fraction
N.B. \(X =\) is not needed BUT
A0 for \(F\) (or \(P\) or horizontal force) = a correct answer if they don’t go on to state \(X = \ldots\)
If they obtain the correct answer for \(F\) and they have said \(F = X\) they can score A1.
N.B. 1.4, 1.40 or \(\frac{1}{7}g\) with no working, scores M1A1