| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Single angled force - find limiting friction or coefficient |
| Difficulty | Standard +0.3 This is a standard two-part friction problem requiring resolution of forces and application of F=ma. Part (a) uses limiting friction (μR) with the particle on the point of moving, while part (b) applies Newton's second law with given acceleration. Both parts follow routine mechanics procedures with straightforward arithmetic, making this slightly easier than average for A-level mechanics questions. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| 5(a) | Attempt at resolving in at least one direction | *M1 |
| Answer | Marks | Guidance |
|---|---|---|
| F=Tcos30 | A1 | Both correct. |
| Use of F=0.5R to form an equation in T or R only | *DM1 | Allow sign errors in R; allow consistent sin/cos mix in R but no |
| Answer | Marks | Guidance |
|---|---|---|
| Attempt to solve for T | DM1 | Allow consistent sin/cos mix and allow sign errors. Must get to |
| Answer | Marks | Guidance |
|---|---|---|
| T =53.8 N | A1 | 53.7622 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 5(b) | Tcos30−F=120.2 | *M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Use of F=0.5R to form an equation in T and solve | DM1 | Must be a two term R as a linear combination of weight and a |
| Answer | Marks | Guidance |
|---|---|---|
| T =55.9 N | A1 | T =55.9127 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 5:
--- 5(a) ---
5(a) | Attempt at resolving in at least one direction | *M1 | Correct number of relevant terms with T resolved; allow sign
errors; allow sin/cos mix.
Can score M1 for any F =Tcos30.
Do not allow g missing in the equation for R. Must have 12, not
just m.
Could see R as part of an equation for F. E.g.
F =0.5(12g−Tsin30) .
R+Tsin30=12g
F=Tcos30 | A1 | Both correct.
Use of F=0.5R to form an equation in T or R only | *DM1 | Allow sign errors in R; allow consistent sin/cos mix in R but no
other errors. Must be two term R as a linear combination of weight
and a component of T, and F must be a single term which is a
component of T. Do not allow g missing.
3
If correct Tcos30=0.5(120−Tsin30) or T =60−0.25T.
2
If no working shown to eliminate T or R, then DM2 for getting T
value correct for their equations and A1 if fully correct. Could use
0.5R=Tcos30 and solve simultaneously.
Attempt to solve for T | DM1 | Allow consistent sin/cos mix and allow sign errors. Must get to
'T='.
Dependent on both previous M1s.
T =53.8 N | A1 | 53.7622
Note: For sign errors:
R−Tsin30=12g answer should be 97.3985…
R−Tsin30=−12g answer should be -97.3985…
R+Tsin30=−12g answer should be -53.7622……
Each of the above would usually get M1A0M1M1A0.
5
Question | Answer | Marks | Guidance
--- 5(b) ---
5(b) | Tcos30−F=120.2 | *M1 | Attempt at N2L; correct number of relevant terms with T resolved;
allow sign errors; allow sin/cos mix, but can be F or any
reasonable attempt at friction.
Use of F=0.5R to form an equation in T and solve | DM1 | Must be a two term R as a linear combination of weight and a
component of T. Allow sign errors and consistent sin/cos mix.
Must get to 'T='.
The equations if correct should be
Tcos30−0.5(120−Tsin30)=120.2
3 3
or T −60+0.25T =2.4 or T +0.25=62.4 and these
2 2
must be solved.
Any use of T or R from part (a) scores DM0 here.
T =55.9 N | A1 | T =55.9127
Note: For sign errors:
R−Tsin30=12g answer should be 101.294…
R−Tsin30=−12g answer should be –93.5026…
R+Tsin30=−12g answer should be –51.6117…
Each of the above would usually get M1M1A0.
3
Question | Answer | Marks | Guidance\includegraphics{figure_5}
A particle of mass 12 kg is going to be pulled across a rough horizontal plane by a light inextensible string. The string is at an angle of 30° above the plane and has tension $T$ N (see diagram). The coefficient of friction between the particle and the plane is 0.5.
\begin{enumerate}[label=(\alph*)]
\item Given that the particle is on the point of moving, find the value of $T$. [5]
\item Given instead that the particle is accelerating at 0.2 ms$^{-2}$, find the value of $T$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2024 Q5 [8]}}