| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Connected particles with friction |
| Difficulty | Standard +0.8 This is a challenging three-part connected particles problem requiring analysis of friction at two interfaces simultaneously, with the constraint that block B remains in equilibrium while P moves on it. Part (iii) requires finding a range of friction coefficients by considering limiting cases (maximum and minimum friction needed), which goes beyond standard textbook exercises and requires careful force analysis and inequality reasoning. |
| Spec | 3.03l Newton's third law: extend to situations requiring force resolution3.03o Advanced connected particles: and pulleys3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Single attempt addressing correct scenario | Credit whether presented first or second | |
| B1 ft mark | B1 ft | Correct inequality sign attached to \(\mu\) value which has been marked |
## Question 7(iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Single attempt addressing correct scenario | | Credit whether presented first or second |
| B1 ft mark | B1 ft | Correct inequality sign attached to $\mu$ value which has been marked |7\\
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A block $B$ is placed on a plane inclined at $30 ^ { \circ }$ to the horizontal. A particle $P$ of mass 0.6 kg is placed on the upper surface of $B$. The particle $P$ is attached to one end of a light inextensible string which passes over a smooth pulley fixed to the top of the plane. A particle $Q$ of mass 0.5 kg is attached to the other end of the string. The portion of the string attached to $P$ is parallel to a line of greatest slope of the plane, the portion of the string attached to $Q$ is vertical and the string is taut. The particles are released from rest and start to move with acceleration $1.4 \mathrm {~ms} ^ { - 2 }$ (see diagram). It is given that $B$ is in equilibrium while $P$ moves on its upper surface.\\
(i) Find the tension in the string while $P$ and $B$ are in contact.\\
(ii) Calculate the coefficient of friction between $P$ and $B$.\\
(iii) Given that the weight of $B$ is 7 N , calculate the set of possible values of the coefficient of friction between $B$ and the plane.
\hfill \mbox{\textit{OCR M1 2013 Q7 [15]}}