CAIE Further Paper 3 2022 June — Question 1 5 marks

Exam BoardCAIE
ModuleFurther Paper 3 (Further Paper 3)
Year2022
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicHooke's law and elastic energy
TypeElastic string equilibrium and statics
DifficultyStandard +0.3 This is a straightforward equilibrium problem with elastic strings requiring resolution of forces in two directions and application of Hooke's law. The setup is standard (particle in equilibrium under three forces), and the solution follows a routine method: resolve horizontally and vertically to find tension and angle, then use Hooke's law to find extension and hence the vertical distance. While it's a Further Maths mechanics question, it requires only basic techniques with no novel insight or complex multi-step reasoning.
Spec3.03n Equilibrium in 2D: particle under forces6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^2
\includegraphics{figure_1} A particle of weight 10 N is attached to one end of a light elastic string. The other end of the string is attached to a fixed point \(A\) on a horizontal ceiling. A horizontal force of 7.5 N acts on the particle. In the equilibrium position, the string makes an angle \(\theta\) with the ceiling (see diagram). The string has natural length 0.8 m and modulus of elasticity 50 N.
  1. Find the tension in the string. [2]
  2. Find the vertical distance between the particle and the ceiling. [3]
Question 1:
AnswerMarks Guidance
1(a)Tcos7.5, Tsin10 B1
1
AnswerMarks
T   7.52 102 2 = 12.5 NB1
2
AnswerMarks
1(b)50x
Hooke’s law: T  , x0.2
AnswerMarks
0.8B1
10
x0.8sin1
AnswerMarks
12.5M1
4
Vertical distance 0.8
AnswerMarks
5A1
3
AnswerMarks Guidance
QuestionAnswer Marks 
Question 1:
--- 1(a) ---
1(a) | Tcos7.5, Tsin10 | B1
1
T   7.52 102 2 = 12.5 N | B1
2
--- 1(b) ---
1(b) | 50x
Hooke’s law: T  , x0.2
0.8 | B1
10
x0.8sin1
12.5 | M1
4
Vertical distance 0.8
5 | A1
3
Question | Answer | Marks | Guidance
\includegraphics{figure_1}

A particle of weight 10 N is attached to one end of a light elastic string. The other end of the string is attached to a fixed point $A$ on a horizontal ceiling. A horizontal force of 7.5 N acts on the particle. In the equilibrium position, the string makes an angle $\theta$ with the ceiling (see diagram). The string has natural length 0.8 m and modulus of elasticity 50 N.

\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string. [2]

\item Find the vertical distance between the particle and the ceiling. [3]
\end{enumerate}

\hfill \mbox{\textit{CAIE Further Paper 3 2022 Q1 [5]}}
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