CAIE M1 2022 November — Question 4 9 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2022
SessionNovember
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeString at angle to slope
DifficultyStandard +0.3 This is a standard mechanics problem requiring resolution of forces in two directions on an inclined plane with friction. Part (a) involves systematic application of Newton's second law with multiple force components (7 marks suggests routine working), while part (b) is a straightforward kinematics calculation using constant acceleration equations. The problem requires no novel insight—just careful bookkeeping of force components and standard techniques taught in M1.
Spec3.02d Constant acceleration: SUVAT formulae3.03e Resolve forces: two dimensions3.03v Motion on rough surface: including inclined planes
\includegraphics{figure_4} A block of mass 8 kg is placed on a rough plane which is inclined at an angle of 18° to the horizontal. The block is pulled up the plane by a light string that makes an angle of 26° above a line of greatest slope. The tension in the string is \(T\) N (see diagram). The coefficient of friction between the block and plane is 0.65.
  1. The acceleration of the block is 0.2 m s\(^{-2}\). Find \(T\). [7]
  2. The block is initially at rest. Find the distance travelled by the block during the fourth second of motion. [2]
Question 4:
AnswerMarks
4Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
AnswerMarks Guidance
4(a)Attempt at N2L parallel to the plane *M1
Allow sign errors, sin/cos mix, allow g
missing.
AnswerMarks Guidance
Tcos26−8gsin18−F =80.2A1 Allow with their F .
Attempt at resolving perpendicular to the plane*M1 3 terms
Allow sign errors, sin/cos mix, allow g
missing.
AnswerMarks Guidance
R+Tsin26=8gcos18A1
Use of F =0.65R to get an equation in T onlyDM1 R is a linear combination of a component of T
and a component of weight.
Using equations with no missing terms.
AnswerMarks Guidance
Solve for TM1 Dependent on all 3 previous M marks.
T =64 ( .0 ) NA1
7
AnswerMarks
4(b)Complete method to find s using constant acceleration formula(e)
 1 1 1 1 
s= 0.242− 0.232 OR s= ( 0+0.24 )4− ( 0+0.23 )3
 
AnswerMarks Guidance
 2 2 2 2 M1 Finding distance moved between t =3 and
t =4, must be using a=0.2
AnswerMarks Guidance
Distance = 0.7 mA1 If 0 marks scored then
 1 
SCB1 for s = 0.242 =1.6
 
 2 
2
AnswerMarks Guidance
QuestionAnswer Marks 
Question 4:
4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
--- 4(a) ---
4(a) | Attempt at N2L parallel to the plane | *M1 | 4 terms.
Allow sign errors, sin/cos mix, allow g
missing.
Tcos26−8gsin18−F =80.2 | A1 | Allow with their F .
Attempt at resolving perpendicular to the plane | *M1 | 3 terms
Allow sign errors, sin/cos mix, allow g
missing.
R+Tsin26=8gcos18 | A1
Use of F =0.65R to get an equation in T only | DM1 | R is a linear combination of a component of T
and a component of weight.
Using equations with no missing terms.
Solve for T | M1 | Dependent on all 3 previous M marks.
T =64 ( .0 ) N | A1
7
--- 4(b) ---
4(b) | Complete method to find s using constant acceleration formula(e)
 1 1 1 1 
s= 0.242− 0.232 OR s= ( 0+0.24 )4− ( 0+0.23 )3
 
 2 2 2 2  | M1 | Finding distance moved between t =3 and
t =4, must be using a=0.2
Distance = 0.7 m | A1 | If 0 marks scored then
 1 
SCB1 for s = 0.242 =1.6
 
 2 
2
Question | Answer | Marks | Guidance
\includegraphics{figure_4}

A block of mass 8 kg is placed on a rough plane which is inclined at an angle of 18° to the horizontal. The block is pulled up the plane by a light string that makes an angle of 26° above a line of greatest slope. The tension in the string is $T$ N (see diagram). The coefficient of friction between the block and plane is 0.65.

\begin{enumerate}[label=(\alph*)]
\item The acceleration of the block is 0.2 m s$^{-2}$.

Find $T$. [7]

\item The block is initially at rest.

Find the distance travelled by the block during the fourth second of motion. [2]
\end{enumerate}

\hfill \mbox{\textit{CAIE M1 2022 Q4 [9]}}
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