Moderate -0.8 This is a standard two-particle pulley system requiring application of Newton's second law to both masses and solving simultaneous equations. It's a routine mechanics exercise with straightforward setup and calculation, requiring fewer steps than average A-level questions and testing only basic application of F=ma with no problem-solving insight needed.
Two particles, of masses \(1.8\) kg and \(1.2\) kg, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest.
Find the magnitude of the acceleration of the particles and find the tension in the string. [4]
Use of Newton’s second law for either particle or system
*M1
correct.
T −1.2g =1.2a
1.8g−T =1.8a
Answer
Marks
Guidance
1.8g−1.2g =(1.2+1.8)a
A1
For any 2 correct equations.
For attempt to solve for T
DM1
From equations with the correct number of relevant terms.
If a found first, then substituting into an equation with the correct
number of relevant terms and solving.
a=2ms−2
Answer
Marks
Guidance
T =14.4N
A1
Both correct.
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | Use of Newton’s second law for either particle or system | *M1 | Correct number of terms; allow sign errors. Dimensionally
correct.
T −1.2g =1.2a
1.8g−T =1.8a
1.8g−1.2g =(1.2+1.8)a | A1 | For any 2 correct equations.
For attempt to solve for T | DM1 | From equations with the correct number of relevant terms.
If a found first, then substituting into an equation with the correct
number of relevant terms and solving.
a=2ms−2
T =14.4N | A1 | Both correct.
4
Question | Answer | Marks | Guidance
Two particles, of masses $1.8$ kg and $1.2$ kg, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest.
Find the magnitude of the acceleration of the particles and find the tension in the string. [4]
\hfill \mbox{\textit{CAIE M1 2024 Q1 [4]}}