| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2003 |
| Session | June |
| Marks | 11 |
| 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 M1 mechanics problem requiring routine application of Newton's second law on an inclined plane with friction, followed by kinematics. The steps are straightforward: resolve forces perpendicular to find normal reaction, calculate friction force, apply F=ma parallel to slope, then use v²=u²+2as. No novel insight required, slightly easier than average due to being a textbook-style two-part question with given values. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| \(R(\nwarrow)\): \(R = 3g\cos 30° = 25.46\) N | M1 A1 | |
| \(F = 0.4R \approx 10.2\) N | M1 A1 | accept 10 N, (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| \(R(\nearrow)\): \(-F + 3g\sin 30° = 3a\) | M1 A2 | \(-1\) eeoo |
| \(\Rightarrow a \approx 8.3\) m s\(^{-2}\) | M1 A1 | |
| \(v^2 = u^2 + 2as\): \(6^2 = 2 \times a \times s\) | M1 | |
| \(\Rightarrow s \approx 2.17\) m | A1 | accept 2.2 m, (7) |
# Question 6:
## Part (a):
| Working | Marks | Notes |
|---------|-------|-------|
| $R(\nwarrow)$: $R = 3g\cos 30° = 25.46$ N | M1 A1 | |
| $F = 0.4R \approx 10.2$ N | M1 A1 | accept 10 N, (4) |
## Part (b):
| Working | Marks | Notes |
|---------|-------|-------|
| $R(\nearrow)$: $-F + 3g\sin 30° = 3a$ | M1 A2 | $-1$ eeoo |
| $\Rightarrow a \approx 8.3$ m s$^{-2}$ | M1 A1 | |
| $v^2 = u^2 + 2as$: $6^2 = 2 \times a \times s$ | M1 | |
| $\Rightarrow s \approx 2.17$ m | A1 | accept 2.2 m, (7) |
---6. A particle $P$ of mass 3 kg is projected up a line of greatest slope of a rough plane inclined at an angle of $30 ^ { \circ }$ to the horizontal. The coefficient of friction between $P$ and the plane is 0.4 . The initial speed of P is $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find
\begin{enumerate}[label=(\alph*)]
\item the frictional force acting on $P$ as it moves up the plane,
\item the distance moved by $P$ up the plane before $P$ comes to instantaneous rest.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2003 Q6 [11]}}