CAIE M1 2015 November — Question 1 3 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2015
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPulley systems
TypeTwo particles over pulley, vertical strings
DifficultyModerate -0.8 This is a straightforward statics problem requiring only basic equilibrium principles. Students must recognize that tension equals the weight of the hanging particle (3g), then resolve forces perpendicular to the plane using the given cosine value. It involves standard techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires careful resolution of forces on an inclined plane.
Spec3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 0

1 \includegraphics[max width=\textwidth, alt={}, center]{f23ea8e7-9b81-4192-8c20-8c46aabfecca-2_446_497_258_826} A small ball \(B\) of mass 4 kg is attached to one end of a light inextensible string. A particle \(P\) of mass 3 kg is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. \(B\) is at rest on a rough plane inclined to the horizontal at an angle of \(\alpha\), where \(\cos \alpha = 0.8\) (see diagram). State the tension in the string and find the normal component of the contact force exerted on \(B\) by the plane.

Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Tension is 30 NB1
\(R = (4g - 30) \times 0.8\)M1 For resolving forces acting on \(B\), perpendicular to the plane
Normal component is 8 NA1 Total: 3 marks
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Tension is 30 N | B1 | |
| $R = (4g - 30) \times 0.8$ | M1 | For resolving forces acting on $B$, perpendicular to the plane |
| Normal component is 8 N | A1 | Total: 3 marks |

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\includegraphics[max width=\textwidth, alt={}, center]{f23ea8e7-9b81-4192-8c20-8c46aabfecca-2_446_497_258_826}

A small ball $B$ of mass 4 kg is attached to one end of a light inextensible string. A particle $P$ of mass 3 kg is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. $B$ is at rest on a rough plane inclined to the horizontal at an angle of $\alpha$, where $\cos \alpha = 0.8$ (see diagram). State the tension in the string and find the normal component of the contact force exerted on $B$ by the plane.

\hfill \mbox{\textit{CAIE M1 2015 Q1 [3]}}