| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Particle on inclined plane - force parallel to slope |
| Difficulty | Moderate -0.3 This is a standard two-part friction problem requiring resolution of forces parallel and perpendicular to an inclined plane. Part (i) involves straightforward application of equilibrium conditions (F=μR) with the block on the point of sliding down. Part (ii) requires recognizing that maximum X occurs when the block is about to slide up the plane, reversing the friction direction. While it involves multiple steps and careful sign management, it follows a well-practiced textbook template with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| 3(i) | R=3gcos 60 | B1 |
| Use F=µR | M1 | |
| [3gsin60 – µ3gcos60 – 15=0] | M1 | Resolve forces parallel to the plane, 3 terms |
| A1 | Correct equation | |
| µ =0.732 | A1 | Allow µ= 3−1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | [Maximum force = 3gsin60+F | |
| = 3 sin60 + µ3gcos60] | M1 | |
| X=37(.0) | A1 | ( ) |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | R=3gcos 60 | B1
Use F=µR | M1
[3gsin60 – µ3gcos60 – 15=0] | M1 | Resolve forces parallel to the plane, 3 terms
A1 | Correct equation
µ =0.732 | A1 | Allow µ= 3−1
5
--- 3(ii) ---
3(ii) | [Maximum force = 3gsin60+F
= 3 sin60 + µ3gcos60] | M1
X=37(.0) | A1 | ( )
AllowX =15 2 3−1
2
Question | Answer | Marks | GuidanceA block of mass 3 kg is at rest on a rough plane inclined at 60° to the horizontal. A force of magnitude 15 N acting up a line of greatest slope of the plane is just sufficient to prevent the block from sliding down the plane.
\begin{enumerate}[label=(\roman*)]
\item Find the coefficient of friction between the block and the plane. [5]
\end{enumerate}
The force of magnitude 15 N is now replaced by a force of magnitude $X$ N acting up the line of greatest slope.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the greatest value of $X$ for which the block does not move. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2019 Q3 [7]}}