| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Heavier particle hits ground, lighter continues upward - vertical strings |
| Difficulty | Challenging +1.2 This is a multi-stage pulley problem requiring students to analyze three distinct phases: initial motion with both particles, motion after Q hits the ground, and Q's subsequent upward motion until the string becomes taut again. While it involves several steps and careful tracking of velocities/positions across phases, the mechanics are standard M1 techniques (Newton's second law, SUVAT equations, energy considerations). The conceptual demand is moderate—recognizing when to switch between connected and independent motion—but no novel insight is required beyond systematic application of familiar methods. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(h = \frac{1}{2} \times 0.5 \times 2\) | M1 | For using area property of the graph or constant acceleration formulae |
| \(h = 0.5\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(a = 2 \div 0.5\) | B1 | State the value of \(a\) using the gradient property of the graph |
| \(T - mg = ma\) and \((1-m)g - T = (1-m)a\), or \(a = \{(1-2m) \div (1-m+m)\}g\) | M1 | For applying Newton's 2nd law to \(P\) (while \(Q\) is moving) and Newton's 2nd law to \(Q\) (while \(Q\) is moving), or using \(a = \frac{(M-m)}{(M+m)}g\) |
| (eliminate \(T\) or rearrange to find \(m\)) | M1 | |
| \(m = 0.3\) | A1 | |
| \(T - 0.3 \times 10 = 4 \times 0.3\) or \(0.7 \times 10 - T = 4 \times 0.7\) | M1 | For substituting \(a\) and \(m\) into Newton's 2nd law for \(P\) or \(Q\) to find \(T\) |
| Tension is \(4.2\) N | A1 | [6] |
## Question 6:
### Part (i)
| Working/Answer | Mark | Guidance |
|---|---|---|
| $h = \frac{1}{2} \times 0.5 \times 2$ | M1 | For using area property of the graph or constant acceleration formulae |
| $h = 0.5$ | A1 | **[2]** |
### Part (ii)
| Working/Answer | Mark | Guidance |
|---|---|---|
| $a = 2 \div 0.5$ | B1 | State the value of $a$ using the gradient property of the graph |
| $T - mg = ma$ and $(1-m)g - T = (1-m)a$, or $a = \{(1-2m) \div (1-m+m)\}g$ | M1 | For applying Newton's 2nd law to $P$ (while $Q$ is moving) and Newton's 2nd law to $Q$ (while $Q$ is moving), or using $a = \frac{(M-m)}{(M+m)}g$ |
| (eliminate $T$ or rearrange to find $m$) | M1 | |
| $m = 0.3$ | A1 | |
| $T - 0.3 \times 10 = 4 \times 0.3$ or $0.7 \times 10 - T = 4 \times 0.7$ | M1 | For substituting $a$ and $m$ into Newton's 2nd law for $P$ or $Q$ to find $T$ |
| Tension is $4.2$ N | A1 | **[6]** |(i) Find the value of $h$.\\
(ii) Find the value of $m$, and find also the tension in the string while $Q$ is moving.\\
(iii) The string is slack while $Q$ is at rest on the ground. Find the total time from the instant that $P$ is released until the string becomes taut again.
\hfill \mbox{\textit{CAIE M1 2015 Q6 [11]}}