Standard +0.3 This is a standard two-stage pulley problem requiring application of Newton's second law to find acceleration, then kinematics to find speed, followed by energy conservation after B hits the floor. While it involves multiple steps and two phases of motion, the techniques are routine M1 content with no novel insight required—slightly easier than average due to straightforward setup and clear problem structure.
2
\includegraphics[max width=\textwidth, alt={}, center]{fd534430-2619-4078-ad0a-2355e656e121-2_569_519_676_813}
Particle \(A\) of mass 0.2 kg and particle \(B\) of mass 0.6 kg are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley. \(B\) is held at rest at a height of 1.6 m above the floor. \(A\) hangs freely at a height of \(h \mathrm {~m}\) above the floor. Both straight parts of the string are vertical (see diagram). \(B\) is released and both particles start to move. When \(B\) reaches the floor it remains at rest, but \(A\) continues to move vertically upwards until it reaches a height of 3 m above the floor. Find the speed of \(B\) immediately before it hits the floor, and hence find the value of \(h\).
For using \(a = (M-m)g/(M+m)\) or for applying Newton's 2nd law to A and to B and solving for \(a\)
\(a = 5\)
A1
When B reaches the floor: \(v^2 = 2 \times 5 \times 1.6\); speed is \(4\ \text{ms}^{-1}\)
B1ft
ft \(a \neq g\), \(v = \sqrt{3.2a}\)
M1
For using \(0 = u^2 - 2gs\) or PE gain = KE loss
\(0 = 16 - 20s \quad (s = 0.8)\)
A1ft
ft speed
\(h + 1.6 + 0.8 = 3 \Rightarrow h = 0.6\)
B1
6 marks
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| | M1 | For using $a = (M-m)g/(M+m)$ or for applying Newton's 2nd law to A and to B and solving for $a$ |
| $a = 5$ | A1 | |
| When B reaches the floor: $v^2 = 2 \times 5 \times 1.6$; speed is $4\ \text{ms}^{-1}$ | B1ft | ft $a \neq g$, $v = \sqrt{3.2a}$ |
| | M1 | For using $0 = u^2 - 2gs$ or PE gain = KE loss |
| $0 = 16 - 20s \quad (s = 0.8)$ | A1ft | ft speed |
| $h + 1.6 + 0.8 = 3 \Rightarrow h = 0.6$ | B1 | 6 marks |
---
2\\
\includegraphics[max width=\textwidth, alt={}, center]{fd534430-2619-4078-ad0a-2355e656e121-2_569_519_676_813}
Particle $A$ of mass 0.2 kg and particle $B$ of mass 0.6 kg are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley. $B$ is held at rest at a height of 1.6 m above the floor. $A$ hangs freely at a height of $h \mathrm {~m}$ above the floor. Both straight parts of the string are vertical (see diagram). $B$ is released and both particles start to move. When $B$ reaches the floor it remains at rest, but $A$ continues to move vertically upwards until it reaches a height of 3 m above the floor. Find the speed of $B$ immediately before it hits the floor, and hence find the value of $h$.
\hfill \mbox{\textit{CAIE M1 2013 Q2 [6]}}