| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Connected particles with friction |
| Difficulty | Standard +0.3 This is a standard M1 connected particles problem with friction on an inclined plane. While it involves multiple steps (resolving forces, applying F=μR, Newton's second law to both masses, solving simultaneous equations, and kinematics), all techniques are routine for M1. The question guides students through each step explicitly, and the 'show that' format reduces problem-solving demand. Slightly easier than average due to its structured, methodical approach. |
| Spec | 3.03o Advanced connected particles: and pulleys3.03r Friction: concept and vector form |
| Answer | Marks | Guidance |
|---|---|---|
| 7(i) | \(R = 1.5g\cos21°\) | B1 |
| 7(i) | Frictional force is 10.98N | M1 |
| 7(i) | (AG) | A1 |
| 7(i) | [3] | |
| 7(ii) | \(T + 1.5g\sin21° - 10.98 = 1.5a\) | M1 |
| 7(ii) | \(1.2g - T = 1.2a\) | A2 |
| 7(ii) | [5] | |
| 7(iii) | \(T - 1.5a = 5.71\) and \(1.2a + T = 11.76\) | M1 |
| 7(iii) | \(a = 2.24\) | (AG) |
| 7(iii) | [2] | |
| 7(iv) | \(v^2 = 2 × 2.24 × 2\) | M1 |
| 7(iv) | Speed of the block is 2.99ms⁻¹ | A1 |
| 7(iv) | [2] | |
| 7(ivb) | \(a = -3.81\) | M1 |
| 7(ivb) | \(v^2 = 2.99^2 + 2 × (-3.81) × 0.8\) | M1 |
| 7(ivb) | Speed of the block is 1.69ms⁻¹ | A1 |
| 7(ivb) | [4] |
7(i) | $R = 1.5g\cos21°$ | B1 |
7(i) | Frictional force is 10.98N | M1 | For using $F = \mu R$
7(i) | (AG) | A1 | Note 1.2gcos21=10.98 fortuitously, B0M0A0
7(i) | | [3] |
7(ii) | $T + 1.5g\sin21° - 10.98 = 1.5a$ | M1 | For obtaining an N2L equation relating to the block in which F, T, m and a are in linear combination or For obtaining an N2L equation relating to the object in which T, m and a are in linear combination
7(ii) | $1.2g - T = 1.2a$ | A2 | -A1 for each error to zero
7(ii) | | [5] | Error is a wrong/omitted term, failure to substitute a numerical value for a letter (excluding g), excess terms. Minimise error count.
7(iii) | $T - 1.5a = 5.71$ and $1.2a + T = 11.76$ | M1 | For solving the simultaneous equations in T and a for a.
7(iii) | $a = 2.24$ | (AG) | A1 | Evidence of solving needed
7(iii) | | [2] |
7(iv) | $v^2 = 2 × 2.24 × 2$ | M1 | For using $v^2 = 2as$ with cv (a) or 2.24
7(iv) | Speed of the block is 2.99ms⁻¹ | A1 | Accept 3
7(iv) | | [2] |
7(ivb) | $a = -3.81$ | M1 | For using $T = 0$ to find a
7(ivb) | $v^2 = 2.99^2 + 2 × (-3.81) × 0.8$ | M1 | For using $v^2 = u^2 + 2as$ with cv(2.99) and s = 2.8 - 2 and any value for a
7(ivb) | Speed of the block is 1.69ms⁻¹ | A1 | Accept art 1.7 from correct work
7(ivb) | | [4] |7\\
\includegraphics[max width=\textwidth, alt={}, center]{ae5d1e27-5853-48aa-9046-86ce1c1a154a-5_488_739_269_703}
One end of a light inextensible string is attached to a block of mass 1.5 kg . The other end of the string is attached to an object of mass 1.2 kg . The block is held at rest in contact with a rough plane inclined at $21 ^ { \circ }$ to the horizontal. The string is taut and passes over a small smooth pulley at the bottom edge of the plane. The part of the string above the pulley is parallel to a line of greatest slope of the plane and the object hangs freely below the pulley (see diagram). The block is released and the object moves vertically downwards with acceleration $\mathrm { am } \mathrm { s } ^ { - 2 }$. The tension in the string is TN . The coefficient of friction between the block and the plane is 0.8 .\\
(i) Show that the frictional force acting on the block has magnitude 10.98 N , correct to 2 decimal places.\\
(ii) By applying Newton's second law to the block and to the object, find a pair of simultaneous equations in T and a .\\
(iii) Hence show that $\mathrm { a } = 2.24$, correct to 2 decimal places.\\
(iv) Given that the object is initially 2 m above a horizontal floor and that the block is 2.8 m from the pulley, find the speed of the block at the instant when
\begin{enumerate}[label=(\alph*)]
\item the object reaches the floor,
\item the block reaches the pulley.
{}\\
7
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2007 Q7 [16]}}