| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Particle just remains at rest |
| Difficulty | Standard +0.3 This is a standard M1 mechanics problem requiring resolution of forces on an inclined plane and application of friction laws. Part (i) uses N=mg cos α, part (ii) applies F=ma with friction opposing motion, and part (iii) compares limiting friction with the component down the slope—all routine techniques with straightforward arithmetic given the numerical values. |
| Spec | 3.03i Normal reaction force3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i) | ||
| \([1.2 = mg \cos\alpha]\) | M1 | For resolving forces normal to the plane |
| Mass is 0.125 kg | A1 | 2 |
| Part (ii) | ||
| \([-mg \sin\alpha - F = ma]\) | M1 | For using Newton's second law |
| \(- 0.125 \times 10 \times 0.28 - 0.4 = -0.125a\) | A1ft | |
| \(a = -6 \Rightarrow\) deceleration is 6 m s\(^{-2}\) | A1 | 3 |
| Part (iii) | ||
| \(\mu R > mg \sin\alpha \Rightarrow\) particle remains at rest | M1 | For comparing magnitudes of \(\mu R\) (0.4) and \(mg \sin\alpha\) (0.35) |
| A1 | 2 |
| **Part (i)** | | |
|---|---|---|
| $[1.2 = mg \cos\alpha]$ | M1 | For resolving forces normal to the plane |
| Mass is 0.125 kg | A1 | 2 |
| **Part (ii)** | | |
|---|---|---|
| $[-mg \sin\alpha - F = ma]$ | M1 | For using Newton's second law |
| $- 0.125 \times 10 \times 0.28 - 0.4 = -0.125a$ | A1ft | |
| $a = -6 \Rightarrow$ deceleration is 6 m s$^{-2}$ | A1 | 3 | ft incorrect mass |
| **Part (iii)** | | |
|---|---|---|
| $\mu R > mg \sin\alpha \Rightarrow$ particle remains at rest | M1 | For comparing magnitudes of $\mu R$ (0.4) and $mg \sin\alpha$ (0.35) |
| | A1 | 2 |4 A particle moves up a line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\cos \alpha = 0.96$ and $\sin \alpha = 0.28$.\\
(i) Given that the normal component of the contact force acting on the particle has magnitude 1.2 N , find the mass of the particle.\\
(ii) Given also that the frictional component of the contact force acting on the particle has magnitude 0.4 N , find the deceleration of the particle.
The particle comes to rest on reaching the point $X$.\\
(iii) Determine whether the particle remains at $X$ or whether it starts to move down the plane.
\hfill \mbox{\textit{CAIE M1 2009 Q4 [7]}}