| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Coefficient of friction from motion |
| Difficulty | Moderate -0.3 This is a straightforward mechanics problem requiring standard application of Newton's second law on an inclined plane. Students use kinematics to find acceleration (a = v/t = 0.4 m/s²), then resolve forces parallel to the plane (mg sin 20° - F = ma) to verify the given friction value, and finally use F = μR with R = mg cos 20° to find μ. All steps are routine textbook procedures with no conceptual challenges beyond basic force resolution. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(2 = 5a \rightarrow a = 0.4\text{ ms}^{-2}\) | B1 | |
| \([0.1g\sin20 - F = 0.1 \times 0.4]\) | M1 | For applying Newton's 2nd law to the particle |
| \(F = 0.302\text{ N}\) | A1 AG | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([R = 0.1g\cos20\ (= 0.9397)]\) | M1 | For attempting to find \(R\) and using \(\mu = F/R\) |
| \(\mu = 0.3020/0.9397 = 0.321\) | A1 | [2] |
## Question 2(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $2 = 5a \rightarrow a = 0.4\text{ ms}^{-2}$ | B1 | |
| $[0.1g\sin20 - F = 0.1 \times 0.4]$ | M1 | For applying Newton's 2nd law to the particle |
| $F = 0.302\text{ N}$ | A1 AG | [3] |
## Question 2(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[R = 0.1g\cos20\ (= 0.9397)]$ | M1 | For attempting to find $R$ and using $\mu = F/R$ |
| $\mu = 0.3020/0.9397 = 0.321$ | A1 | [2] |
---2 A particle of mass 0.1 kg is released from rest on a rough plane inclined at $20 ^ { \circ }$ to the horizontal. It is given that, 5 seconds after release, the particle has a speed of $2 \mathrm {~ms} ^ { - 1 }$.\\
(i) Find the acceleration of the particle and hence show that the magnitude of the frictional force acting on the particle is 0.302 N , correct to 3 significant figures.\\
(ii) Find the coefficient of friction between the particle and the plane.
\hfill \mbox{\textit{CAIE M1 2016 Q2 [5]}}