CAIE M1 2010 November — Question 1 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2010
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFriction
TypeSingle angled force - find limiting friction or coefficient
DifficultyModerate -0.8 This is a straightforward mechanics problem requiring standard application of resolving forces and the limiting friction formula F = μR. The setup is simple (horizontal surface, single angled force), and the solution involves routine resolution of forces vertically and horizontally followed by direct calculation of μ. Easier than average due to minimal problem-solving required.
Spec3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces
1 A block of mass 400 kg rests in limiting equilibrium on horizontal ground. A force of magnitude 2000 N acts on the block at an angle of \(15 ^ { \circ }\) to the upwards vertical. Find the coefficient of friction between the block and the ground, correct to 2 significant figures.
AnswerMarks Guidance
\(R + 2000\cos15° = 400\text{ g}\)M1 For resolving forces vertically (3 terms required)
\(F = 2000\sin 15°\)A1
\([2000\sin15° = \mu(400g - 2000\cos15°)]\)M1 For using \(F = \mu R\)
Coefficient is 0.25A1 [5]
SR(max. 4/5) for candidates who either: have sin and cos interchanged or have angle \(15°\) above the horizontal
AnswerMarks Guidance
\(R + 2000\sin15° = 400\text{ g and } F = 2000\cos15°\)M1 For resolving forces vertically
\([2000\cos15° = \mu(400g - 2000\sin15°)]\)M1 For using \(F = \mu R\)
Coefficient is 0.55A1 
$R + 2000\cos15° = 400\text{ g}$ | M1 | For resolving forces vertically (3 terms required)
$F = 2000\sin 15°$ | A1 |
$[2000\sin15° = \mu(400g - 2000\cos15°)]$ | M1 | For using $F = \mu R$
Coefficient is 0.25 | A1 | [5]

**SR(max. 4/5)** for candidates who either: have sin and cos interchanged or have angle $15°$ above the horizontal

$R + 2000\sin15° = 400\text{ g and } F = 2000\cos15°$ | M1 | For resolving forces vertically
$[2000\cos15° = \mu(400g - 2000\sin15°)]$ | M1 | For using $F = \mu R$
Coefficient is 0.55 | A1 |

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1 A block of mass 400 kg rests in limiting equilibrium on horizontal ground. A force of magnitude 2000 N acts on the block at an angle of $15 ^ { \circ }$ to the upwards vertical. Find the coefficient of friction between the block and the ground, correct to 2 significant figures.

\hfill \mbox{\textit{CAIE M1 2010 Q1 [5]}}
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