| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with force parallel to slope |
| Difficulty | Moderate -0.8 This is a standard M1 equilibrium problem requiring resolution of forces parallel and perpendicular to the plane, with straightforward application of F=μR at limiting equilibrium. Parts (a) and (b) are routine calculations, while part (c) requires comparing μR with the component of weight down the slope—a common textbook exercise with no novel problem-solving required. |
| Spec | 3.03r Friction: concept and vector form3.03s Contact force components: normal and frictional3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks |
|---|---|
| 4 | R |
Question 4:
4 | R
X 2.5g (a) R = 2.5g cos 20 M1
F
≈ 23.0 or 23 N A1
(2)
(b) X = 0.4 x 23.0 + 2.5g sin 20 M1 A2,1,0√
≈ 17.6 or 18 N A1
(4)
(c) R F
In equlib. F = 2.5g sin 20 ≈ 8.38 or 8.4 N B1
2.5g μR = 0.4 x 2.5g cos 20 ≈ 9.21 or 9.2 N B1
8.4 < 9.2 (using ‘F < μR’ not F = μR) M1
Since F < μR remains in equilibrium (cso) A1
(4)\includegraphics{figure_3}
A particle $P$ of mass 2.5 kg rests in equilibrium on a rough plane under the action of a force of magnitude $X$ newtons acting up a line of greatest slope of the plane, as shown in Figure 3. The plane is inclined at 20° to the horizontal. The coefficient of friction between $P$ and the plane is 0.4. The particle is in limiting equilibrium and is on the point of moving up the plane. Calculate
\begin{enumerate}[label=(\alph*)]
\item the normal reaction of the plane on $P$, [2]
\item the value of $X$. [4]
\end{enumerate}
The force of magnitude $X$ newtons is now removed.
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{2}
\item Show that $P$ remains in equilibrium on the plane. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2005 Q4 [10]}}