| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Equilibrium on slope with force parallel to slope |
| Difficulty | Standard +0.3 This is a standard M1 mechanics problem involving forces on a slope with friction. Part (a) requires resolving forces perpendicular and parallel to the plane with limiting friction (F = μR), then solving simultaneous equations. Part (b) uses constant acceleration kinematics (suvat) after finding the net force down the slope. Both parts follow routine textbook procedures with no novel insight required, though the two-part structure and careful force resolution make it slightly above average difficulty for M1. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03e Resolve forces: two dimensions3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks |
|---|---|
| 5 | (a) |
Question 5:
5 | (a)
R F R = 400g cos 15° (≈ 3786 N) B1
T
F = 0.2R used B1
400g T + 0.2R = 400g sin 15° M1 A1
↓
T ≈ 257 or 260 N M1 A1
(6)
(b) 400g sin 15° – 0.2 x 400g cos 15° = 400a M1 A1
a = 0.643(…) A1
50 = 1 x 0.643 x t2 M1 A1√
2
t = 12.5 or 12 s A1
(6)
General rule again about > 3 sf
Weight/mass confusion: treat as MR [ T = 26.3/26; a = 0.0656…; t = 39(.0)]
(b) Allow a = 0.64
(Final M1 not dependent but requires an attempt to find an a which is not assumed to be g)\includegraphics{figure_3}
Figure 3 shows a boat $B$ of mass $400$ kg held at rest on a slipway by a rope. The boat is modelled as a particle and the slipway as a rough plane inclined at $15°$ to the horizontal. The coefficient of friction between $B$ and the slipway is $0.2$. The rope is modelled as a light, inextensible string, parallel to a line of greatest slope of the plane. The boat is in equilibrium and on the point of sliding down the slipway.
\begin{enumerate}[label=(\alph*)]
\item Calculate the tension in the rope. [6]
\end{enumerate}
The boat is $50$ m from the bottom of the slipway. The rope is detached from the boat and the boat slides down the slipway.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the time taken for the boat to slide to the bottom of the slipway. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q5 [12]}}