| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Heavier particle hits ground, lighter continues upward - vertical strings |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with multiple parts requiring kinematics (SUVAT), Newton's laws, and energy conservation. While it has several parts and requires careful tracking of the motion in different phases, each individual step uses routine mechanics techniques without requiring novel insight or complex problem-solving strategies. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = 1.12\) ms\(^{-1}\) | M1, A1, M1, A1, [4] | Uses \(s = 0.5 \times 1.4t^2\); Not 0.45; Uses \(v = 1.4t\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(t = (0.114 + 0.8) = 0.914s\) | M1, A1, M1, A1, [4] | Uses \(0^2 = u^2 - 2gs\) or \(u^2 = 2gs\); Allow verification or 0.064~1.12 |
| Answer | Marks | Guidance |
|---|---|---|
| Scalene triangle, base on t axis right edge steeper and terminates on axis, or crosses axis at t = 0.91 | B1, B1, [2] | NB Award A1 for 0.91 on t axis if total time not given in (ii) |
| Answer | Marks | Guidance |
|---|---|---|
| \(B = 0.525\) | M1, A1, A1, A1, [4] | Uses N2L for A or B with attempt at 2 forces; Either; Not 0.53 |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 4.9\) N | A1, [2], B1, [1] | Uses tension and 0.5g without particle weights; Allow 16.7 |
### Part i
$s = 0.5 \times 1.4 \times 0.8^2$
$s = 0.448$ m
$v = 1.4 \times 0.8$
$v = 1.12$ ms$^{-1}$ | M1, A1, M1, A1, [4] | Uses $s = 0.5 \times 1.4t^2$; Not 0.45; Uses $v = 1.4t$
### Part ii
$0^2 = 1.12^2 - 2 \times 9.8s$
$s = 0.064$ m
$0 = 1.12 - 9.8t$ (t = 0.114s)
$t = (0.114 + 0.8) = 0.914s$ | M1, A1, M1, A1, [4] | Uses $0^2 = u^2 - 2gs$ or $u^2 = 2gs$; Allow verification or 0.064~1.12|-4.9t² and halve t; Allow 0.91 [or 0=1.2t-4.9² and halve t
### Part iii
Scalene triangle, base on t axis right edge steeper and terminates on axis, or crosses axis at t = 0.91 | B1, B1, [2] | NB Award A1 for 0.91 on t axis if total time not given in (ii)
### Part iv
$1.4xA = 9.8x - 5.88$ or $1.4xB = 5.88 - 9.8xB$
$A = 0.7$
$B = 0.525$ | M1, A1, A1, A1, [4] | Uses N2L for A or B with attempt at 2 forces; Either; Not 0.53
### Part vb
$T = 0.5 \times 9.8 + 2 \times 5.88$
$T = 16.66$ N
$T = 4.9$ N | A1, [2], B1, [1] | Uses tension and 0.5g without particle weights; Allow 16.77\\
\includegraphics[max width=\textwidth, alt={}, center]{db77a63a-6ff8-4fe5-bdd0-15afb7eb4866-4_419_419_274_735}
Particles $A$ and $B$ are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The particles are released from rest, with the string taut, and $A$ and $B$ at the same height above a horizontal floor (see diagram). In the subsequent motion, $A$ descends with acceleration $1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and strikes the floor 0.8 s after being released. It is given that $B$ never reaches the pulley.\\
(i) Calculate the distance $A$ moves before it reaches the floor and the speed of $A$ immediately before it strikes the floor.\\
(ii) Show that $B$ rises a further 0.064 m after $A$ strikes the floor, and calculate the total length of time during which $B$ is rising.\\
(iii) Sketch the ( $t , v$ ) graph for the motion of $B$ from the instant it is released from rest until it reaches a position of instantaneous rest.\\
(iv) Before $A$ strikes the floor the tension in the string is 5.88 N . Calculate the mass of $A$ and the mass of $B$.\\
(v) The pulley has mass 0.5 kg , and is held in a fixed position by a light vertical chain. Calculate the tension in the chain
\begin{enumerate}[label=(\alph*)]
\item immediately before $A$ strikes the floor,
\item immediately after $A$ strikes the floor.
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2008 Q7 [17]}}