| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Year | 2021 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Stacked boxes, friction between surfaces |
| Difficulty | Standard +0.8 This is a multi-part connected particles problem requiring analysis of friction limits, separate accelerations when sliding occurs, and a toppling vs sliding analysis involving moments. While the individual calculations are standard A-level mechanics, the combination of three distinct scenarios (especially the toppling analysis in part c) and the need to compare limiting friction with the force required to topple makes this moderately challenging, above average difficulty for A-level Further Mechanics. |
| Spec | 3.03r Friction: concept and vector form3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | If the box and trolley were not to slide, both would have to |
| Answer | Marks | Guidance |
|---|---|---|
| 16 | M1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| to be 15.625 N. | M1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| slide. | A1 | 2.2a |
| Answer | Marks |
|---|---|
| (b) | Let the accelerations be a and a ms-2. |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | Box: 14.7=5a ⇒a =2.94 | |
| B B | B1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | Trolley: 50−14.7=11a ⇒a ≈3.21 | |
| T T | B1 | 1.1 |
| Answer | Marks |
|---|---|
| (c) | At the point of sliding, assuming toppling has not yet |
| Answer | Marks | Guidance |
|---|---|---|
| S =14.7 | B1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| 91T =28⋅5g | M1 | 1.1 |
| ⇒T ≈15.1 | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| so the block will slide. | A1 | 2.4 |
Question 6:
6 | (a) | If the box and trolley were not to slide, both would have to
have an acceleration of 50 =3.125 ms-2.
16 | M1 | 1.1 | Enough to see 3.125 to award this
mark.
So the frictional force of the trolley on the block would have
to be 15.625 N. | M1 | 1.1 | Enough to see 15.625 to award this
mark.
But the maximum friction force on the block
=5g×0.3=14.7N which is not enough, so the block will
slide. | A1 | 2.2a | AG
Only award this mark if some sort
of argument is conveyed as well as
seeing 14.7 or 2.94
[3]
(b) | Let the accelerations be a and a ms-2.
B T
(i) | Box: 14.7=5a ⇒a =2.94
B B | B1 | 1.1
[1]
(ii) | Trolley: 50−14.7=11a ⇒a ≈3.21
T T | B1 | 1.1
[1]
(c) | At the point of sliding, assuming toppling has not yet
occurred, let the force of the obstruction on the block have
magnitude S N.
S =14.7 | B1 | 3.4
At the point of toppling, assuming sliding has not yet
occurred, let the force of the obstruction on the block have
magnitude T N.
Moments about bottom left corner:
91T =28⋅5g | M1 | 1.1
⇒T ≈15.1 | A1 | 1.1
S<T
so the block will slide. | A1 | 2.4 | Conclusion must be stated clearly
in words.
[4]6 Fig. 6.1 shows a cross-section through a block of mass 5 kg which is on top of a trolley of mass 11 kg . The trolley is on top of a smooth horizontal surface. The coefficient of friction between the block and the trolley is 0.3 .
Throughout this question you may assume that there are no other resistances to motion on either the block or the trolley.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-6_339_1317_552_294}
\captionsetup{labelformat=empty}
\caption{Fig. 6.1}
\end{center}
\end{figure}
Initially, both the block and trolley are at rest. A constant force of magnitude 50 N is now applied horizontally to the trolley, as shown in Fig. 6.1.
\begin{enumerate}[label=(\alph*)]
\item Show that in the subsequent motion the block will slide.
\item Find the acceleration of
\begin{enumerate}[label=(\roman*)]
\item the block,
\item the trolley.
The same block and trolley are again at rest. An obstruction, in the form of a fixed horizontal pole, is placed in front of the block, the pole is 91 cm above the trolley and the width of the block is 56 cm as shown in Fig. 6.2, as well as the forward direction of motion.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5c1cfe41-d7a2-4f69-ae79-67d9f023c246-6_426_1324_1793_269}
\captionsetup{labelformat=empty}
\caption{Fig. 6.2}
\end{center}
\end{figure}
It is given that the block is uniform and that the contact between the pole and the block is smooth.
A small horizontal force is now applied to the trolley in the forward direction of motion and gradually increased.
\end{enumerate}\item Determine whether the block will topple or slide.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS 2021 Q6 [9]}}