CAIE M1 2024 June — Question 5 8 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2024
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeParticle on inclined plane - force at angle to slope
DifficultyStandard +0.8 This is a challenging equilibrium problem requiring resolution of forces in two directions on an inclined plane, consideration of limiting friction in two opposite directions (up and down the slope), and solving simultaneous equations twice. It goes beyond standard single-direction friction problems and requires careful geometric reasoning about when friction acts upslope vs downslope, making it moderately harder than average A-level mechanics questions.
Spec3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 03.03v Motion on rough surface: including inclined planes
\includegraphics{figure_5} A particle of mass 0.8 kg lies on a rough plane which is inclined at an angle of \(28°\) to the horizontal. The particle is kept in equilibrium by a force of magnitude \(T\) N. This force acts at an angle of \(35°\) above a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.2. Find the least and greatest possible values of \(T\). [8]
Question 5:
AnswerMarks Guidance
5Attempt at resolving perpendicular to plane to get an equation *M1
allow g missing; m0.8 must be used; correct angles
must be used.
RTsin350.8gcos28 R0.57357 T 7.06358
AnswerMarks
 A1
Attempt to resolve parallel to plane for one of the possible cases to get an
AnswerMarks Guidance
equation*M1 3 relevant terms; allow sign errors; allow sin/cos mix;
allow g missing; m0.8 must be used; correct angles
must be used.
Tcos350.8gsin28F 0.81915T 3.75577F
AnswerMarks Guidance
 A1 May use their F.
Tcos350.8gsin28F 0.81915T 3.75577F
AnswerMarks Guidance
 A1 May use their F.
Use of F 0.2R to get an equation in T onlyDM1 Dependent on previous 2 M marks.
May be implied by correct T value.
Allow g missing.
If resolved equations incorrect and no working seen, then
this mark is implied by the correct T value for their
equations.
AnswerMarks Guidance
Solve to get T 5.53A1 5.534499898
AWRT 5.53 from correct work.
Allow 5.54 from correct work.
AnswerMarks Guidance
Solve to get T 3.33A1 3.326141531
AWRT 3.33 from correct work.
Allow 3.32 from correct work.
8
AnswerMarks Guidance
QuestionAnswer Marks 
Question 5:
5 | Attempt at resolving perpendicular to plane to get an equation | *M1 | 3 relevant terms; allow sign errors; allow sin/cos mix;
allow g missing; m0.8 must be used; correct angles
must be used.
RTsin350.8gcos28 R0.57357 T 7.06358
  | A1
Attempt to resolve parallel to plane for one of the possible cases to get an
equation | *M1 | 3 relevant terms; allow sign errors; allow sin/cos mix;
allow g missing; m0.8 must be used; correct angles
must be used.
Tcos350.8gsin28F 0.81915T 3.75577F
  | A1 | May use their F.
Tcos350.8gsin28F 0.81915T 3.75577F
  | A1 | May use their F.
Use of F 0.2R to get an equation in T only | DM1 | Dependent on previous 2 M marks.
May be implied by correct T value.
Allow g missing.
If resolved equations incorrect and no working seen, then
this mark is implied by the correct T value for their
equations.
Solve to get T 5.53 | A1 | 5.534499898
AWRT 5.53 from correct work.
Allow 5.54 from correct work.
Solve to get T 3.33 | A1 | 3.326141531
AWRT 3.33 from correct work.
Allow 3.32 from correct work.
8
Question | Answer | Marks | Guidance
\includegraphics{figure_5}

A particle of mass 0.8 kg lies on a rough plane which is inclined at an angle of $28°$ to the horizontal. The particle is kept in equilibrium by a force of magnitude $T$ N. This force acts at an angle of $35°$ above a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.2.

Find the least and greatest possible values of $T$. [8]

\hfill \mbox{\textit{CAIE M1 2024 Q5 [8]}}
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