| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion up rough slope |
| Difficulty | Moderate -0.3 This is a standard mechanics problem requiring resolution of forces on an inclined plane and application of Newton's second law followed by kinematics. While it involves multiple steps (resolving perpendicular to find normal reaction, finding friction force, resolving parallel to find net force, then using equations of motion), these are routine procedures for M1 students with no novel insight required. The numerical values are straightforward to work with, making this slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(R = 0.8g\cos 10 = 7.88\) | B1 | |
| \(F = 0.4 \times 8\cos 10 = 3.15\) | M1 | Use \(F = \mu R\) |
| \(-8\sin 10 - 3.2\cos 10 = 0.8a\) | M1 | Newton 2 along the plane |
| \(a = -5.68 \text{ ms}^{-2}\) | A1 | |
| Total: 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(0 = 12^2 - 2 \times 5.68 \times s\) | M1 | Using \(v^2 = u^2 + 2as\) |
| \(s = 144/(2 \times 5.68) = 12.7\) m | A1 | |
| Total: 2 |
## Question 2(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $R = 0.8g\cos 10 = 7.88$ | B1 | |
| $F = 0.4 \times 8\cos 10 = 3.15$ | M1 | Use $F = \mu R$ |
| $-8\sin 10 - 3.2\cos 10 = 0.8a$ | M1 | Newton 2 along the plane |
| $a = -5.68 \text{ ms}^{-2}$ | A1 | |
| **Total: 4** | | |
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## Question 2(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $0 = 12^2 - 2 \times 5.68 \times s$ | M1 | Using $v^2 = u^2 + 2as$ |
| $s = 144/(2 \times 5.68) = 12.7$ m | A1 | |
| **Total: 2** | | |
---2 A particle of mass 0.8 kg is projected with a speed of $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ up a line of greatest slope of a rough plane inclined at an angle of $10 ^ { \circ }$ to the horizontal. The coefficient of friction between the particle and the plane is 0.4 .\\
(i) Find the acceleration of the particle.\\
(ii) Find the distance the particle moves up the plane before coming to rest.\\
\hfill \mbox{\textit{CAIE M1 2017 Q2 [6]}}