Edexcel M3 — Question 2 8 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeElastic string with friction
DifficultyStandard +0.3 This is a standard M3 equilibrium problem requiring resolution of forces, friction law (F = μR), and Hooke's law (T = λx/l). While it involves multiple steps and careful algebra to reach the specific extension value of 17cm, the techniques are routine for M3 students and the question clearly signposts what to show, making it slightly easier than average.
Spec3.03u Static equilibrium: on rough surfaces6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^2

The diagram shows a particle of mass \(0.7\) kg resting on a rough horizontal table. The coefficient of friction between the particle and the table is \(0.25\). A light elastic string, of natural length \(50\) cm and modulus of elasticity \(6.86\) N, is attached to the particle. The string is kept at an angle of \(60°\) to the horizontal and is gradually extended by pulling on it until the particle moves. Show that the particle starts to move when the extension in the string is \(17\) cm. \includegraphics{figure_2} [8 marks]

AnswerMarks Guidance
Vert: \(R + T \sin 60° = 0.7g\)M1 A1 M1 A1
Horiz: \(T \cos 60° = F\)
\(F = 0.25\)R, so \(0.57 = 0.25(6.86 - 0.8667)\)M1 A1
\(T = 2.394\)
\(T = 6.86x + 0.5\), so \(x = 1.196 + 6.86 = 0.174\) m \(= 17\) cmM1 A1 8 marks
Vert: $R + T \sin 60° = 0.7g$ | M1 A1 M1 A1 |
Horiz: $T \cos 60° = F$ | |
$F = 0.25$R, so $0.57 = 0.25(6.86 - 0.8667)$ | M1 A1 |
$T = 2.394$ | |
$T = 6.86x + 0.5$, so $x = 1.196 + 6.86 = 0.174$ m $= 17$ cm | M1 A1 | 8 marks
The diagram shows a particle of mass $0.7$ kg resting on a rough horizontal table. The coefficient of friction between the particle and the table is $0.25$. A light elastic string, of natural length $50$ cm and modulus of elasticity $6.86$ N, is attached to the particle. The string is kept at an angle of $60°$ to the horizontal and is gradually extended by pulling on it until the particle moves. Show that the particle starts to move when the extension in the string is $17$ cm. 

\includegraphics{figure_2}

[8 marks]

\hfill \mbox{\textit{Edexcel M3  Q2 [8]}}