| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2012 |
| Session | June |
| Marks | 6 |
| Topic | Friction |
| Type | Particle on inclined plane - force parallel to slope |
| Difficulty | Moderate -0.3 This is a standard mechanics problem on limiting friction and equilibrium on an inclined plane. It requires straightforward application of resolving forces perpendicular and parallel to the plane, with F = μR for limiting friction. The three parts are routine calculations with no novel problem-solving required, making it slightly easier than average but still requiring proper method. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
**(i)** Resolving perpendicular to the slope — M1
$R = 100\cos35 = 81.9152\ldots$ N
So Max Friction $= \mu R = 16.38\ldots$ N — A1 [2]
**(ii)** Resolving parallel to the slope (friction down the slope) — M1
$P = 100\sin35 + 16.38\ldots = 73.74\ldots$ — A1 [2]
**(iii)** (friction up the slope) — M1
$P = 100\sin35 - 16.38\ldots = 40.97\ldots$ — A1 [2]
**Total: [6]**9\\
\includegraphics[max width=\textwidth, alt={}, center]{f0c32e07-f3a0-4d58-bd00-c266177ceaac-4_430_565_260_790}
The diagram shows a block of wood, weighing 100 N , at rest on a rough plane inclined at $35 ^ { \circ }$ to the horizontal. The coefficient of friction between the block and the plane is 0.2 . A force of $P \mathrm {~N}$ acts on the block up the slope.\\
(i) Find the maximum possible value of the friction acting on the block.\\
(ii) Given that the block is on the point of moving up the slope, find $P$.\\
(iii) Given that the block is on the point of moving down the slope, find $P$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2012 Q9 [6]}}