CAIE M1 2011 November — Question 2 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2011
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPulley systems
TypeForce on pulley from string
DifficultyStandard +0.3 This is a standard two-particle pulley system requiring application of Newton's second law to find tension and acceleration, followed by vector addition to find the resultant force on the pulley. The setup is straightforward with vertical strings, and the method is a textbook exercise in M1 mechanics with no novel problem-solving required, making it slightly easier than average.
Spec3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium

2 Particles \(A\) of mass 0.65 kg and \(B\) of mass 0.35 kg are attached to the ends of a light inextensible string which passes over a fixed smooth pulley. \(B\) is held at rest with the string taut and both of its straight parts vertical. The system is released from rest and the particles move vertically. Find the tension in the string and the magnitude of the resultant force exerted on the pulley by the string.

AnswerMarks Guidance
M1For applying Newton's second law to either particle (3 terms)
\(0.65g - T = 0.65a\) and \(T - 0.35g = 0.35a\)A1 Accept \((0.65 - 0.35)g = (0.65 + 0.35)a\) as an alternative to one of these equations
M1For solving for \(T\)
Tension in the string is 4.55 NA1
Magnitude of resultant is 9.1 NB1ft 5
| | M1 | For applying Newton's second law to either particle (3 terms) |
| $0.65g - T = 0.65a$ and $T - 0.35g = 0.35a$ | A1 | Accept $(0.65 - 0.35)g = (0.65 + 0.35)a$ as an alternative to one of these equations |
| | M1 | For solving for $T$ |
| Tension in the string is 4.55 N | A1 | |
| Magnitude of resultant is 9.1 N | B1ft | 5 |

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2 Particles $A$ of mass 0.65 kg and $B$ of mass 0.35 kg are attached to the ends of a light inextensible string which passes over a fixed smooth pulley. $B$ is held at rest with the string taut and both of its straight parts vertical. The system is released from rest and the particles move vertically. Find the tension in the string and the magnitude of the resultant force exerted on the pulley by the string.

\hfill \mbox{\textit{CAIE M1 2011 Q2 [5]}}