CAIE Further Paper 3 2024 November — Question 3 2 marks

Exam BoardCAIE
ModuleFurther Paper 3 (Further Paper 3)
Year2024
SessionNovember
Marks2
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Mark schemeDownload PDF ↗
TopicHooke's law and elastic energy
TypeVertical elastic string: projected from equilibrium or other point
DifficultyModerate -0.5 This is a continuation part worth only 2 marks asking to find speed using energy conservation after previous setup work. Standard application of elastic energy formula with straightforward calculation - easier than average but requires correct method from part (a).
Spec6.02i Conservation of energy: mechanical energy principle
  1. Hence find the speed of \(P\) when it is \(2 \text{ m}\) below \(O\). [2]
Question 3:
AnswerMarks
3(a)2mg
Hooke’s law: T = extension and T =mg
AnswerMarks Guidance
2M1 Equilibrium position.
Extension = 1 mA1
1 2mg
EPE loss =  (1+d)2
AnswerMarks
2 2B1
mg(2+1+d)
AnswerMarks
Gain in GPE =B1
1
Equate: mg(1+d)2 =mg(3+d)
AnswerMarks Guidance
2M1
d = 5A1 SC: 3 marks for final answer of 5+1 .
SC: 2 marks for final answer of 5+k , k 1 .
6
AnswerMarks
3(b)1 1 2mg
Energy equation: mV2 +mg(1+d)=  (1+d)2
AnswerMarks Guidance
2 2 2M1 GPE, KE, EPE terms.
V2 =g ( d2 −1 ) V = 40 =2 10A1
Alternatively:
Using KE and GPE from 2 m below O to point O
1
mV2 =2mg
AnswerMarks
2M1
V2 =4g V = 40 =2 10A1
2
AnswerMarks Guidance
QuestionAnswer Marks 
Question 3:
--- 3(a) ---
3(a) | 2mg
Hooke’s law: T = extension and T =mg
2 | M1 | Equilibrium position.
Extension = 1 m | A1
1 2mg
EPE loss =  (1+d)2
2 2 | B1
mg(2+1+d)
Gain in GPE = | B1
1
Equate: mg(1+d)2 =mg(3+d)
2 | M1
d = 5 | A1 | SC: 3 marks for final answer of 5+1 .
SC: 2 marks for final answer of 5+k , k 1 .
6
--- 3(b) ---
3(b) | 1 1 2mg
Energy equation: mV2 +mg(1+d)=  (1+d)2
2 2 2 | M1 | GPE, KE, EPE terms.
V2 =g ( d2 −1 ) V = 40 =2 10 | A1
Alternatively:
Using KE and GPE from 2 m below O to point O
1
mV2 =2mg
2 | M1
V2 =4g V = 40 =2 10 | A1
2
Question | Answer | Marks | Guidance
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Hence find the speed of $P$ when it is $2 \text{ m}$ below $O$. [2]
\end{enumerate}

\hfill \mbox{\textit{CAIE Further Paper 3 2024 Q3 [2]}}
This paper (8 questions)
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Q1 5 Q2 5 Q3 6 Q3 2 Q4 3 Q5 4 Q6 3 Q7 4