Edexcel M3 — Question 1 6 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Marks6
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Mark schemeDownload PDF ↗
TopicMotion on a slope
TypeMotion down smooth slope
DifficultyModerate -0.3 This is a standard banked track circular motion problem requiring resolution of forces (weight and normal reaction) and application of F=mv²/r. While it involves multiple steps (resolving horizontally and vertically, eliminating R, solving for v), it follows a well-practiced procedure with no novel insight required. The calculation is straightforward once the standard method is applied, making it slightly easier than average for M3.
Spec6.05c Horizontal circles: conical pendulum, banked tracks
A cyclist travels on a banked track inclined at \(8°\) to the horizontal. He moves in a horizontal circle of radius 10 m at a constant speed of \(v\) ms\(^{-1}\). If there is no sideways frictional force on the cycle, calculate the value of \(v\). [6 marks]
AnswerMarks Guidance
\(R \cos 8° = mg\), \(R \sin 8° = \frac{mv^2}{10}\)M1 A1 M1 A1
\(\frac{v^2}{98} = \tan 8°\)M1 A1
\(\tan 8° = \frac{v^2}{98 \times 10}\)
\(v = 3.71 \text{ ms}^{-1}\) Total: 6 marks 
$R \cos 8° = mg$, $R \sin 8° = \frac{mv^2}{10}$ | M1 A1 M1 A1 |
$\frac{v^2}{98} = \tan 8°$ | M1 A1 |
$\tan 8° = \frac{v^2}{98 \times 10}$ | |
$v = 3.71 \text{ ms}^{-1}$ | | **Total: 6 marks**
A cyclist travels on a banked track inclined at $8°$ to the horizontal. He moves in a horizontal circle of radius 10 m at a constant speed of $v$ ms$^{-1}$. If there is no sideways frictional force on the cycle, calculate the value of $v$. [6 marks]

\hfill \mbox{\textit{Edexcel M3  Q1 [6]}}
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