| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | October |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Standard +0.3 This is a standard M1 pulley system question requiring Newton's second law for connected particles, friction, and basic kinematics. Part (a) involves setting up two force equations and solving simultaneously—routine for M1. Part (b) applies constant acceleration formulae. Part (c) tests conceptual understanding of limiting friction. While multi-step, it follows a well-practiced template with no novel insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| 7(a) | F =mg | B1 |
| For P: m g − k m g = m a Allow m g − T = m a | M1A1 | |
| For Q: k m g − F = m a Allow T − F = m a | M1A1 |
| Answer | Marks |
|---|---|
| Produce an equation in k and only using T = kmg | M1 |
| Answer | Marks |
|---|---|
| 2 | A1 |
| Answer | Marks |
|---|---|
| 7(a) | B1 for F m g = seen e.g. on a diagram |
| Answer | Marks |
|---|---|
| 7(b) | Attempt to find the acceleration. |
| Answer | Marks |
|---|---|
| or g ( k ) − ] | M1 |
| Answer | Marks |
|---|---|
| 2 2 | M1A1 |
| Answer | Marks |
|---|---|
| g(1−) | A1 |
| Answer | Marks |
|---|---|
| 7(b) | M1 Attempt to find the acceleration in terms of g and or g and k or g, |
| Answer | Marks | Guidance |
|---|---|---|
| 7(c) | P or Q (or the system) would not move | B1 |
| Answer | Marks |
|---|---|
| the left or right’ is B0. | DB1 |
| Answer | Marks |
|---|---|
| 7(c) | B1 Correct statement. B0 if incorrect extras. |
Question 7:
--- 7(a) ---
7(a) | F =mg | B1
For P: m g − k m g = m a Allow m g − T = m a | M1A1
For Q: k m g − F = m a Allow T − F = m a | M1A1
Either of these may be replaced by : m g − F = 2 m a (whole system)
Produce an equation in k and only using T = kmg | M1
1
k (1 ) = +
2 | A1
(7)
7(a) | B1 for F m g = seen e.g. on a diagram
M1 Equation of motion for P with correct no. of terms, condone sign
errors
A1 Correct equation (allow -a)
M1 Equation of motion for Q with correct no. of terms, condone sign
errors
A1 Correct equation (allow -a)
N.B. (-a) must be used in both equations
M1 for producing an equation in k and only
A1 oe Must appear in (a)
--- 7(b) ---
7(b) | Attempt to find the acceleration.
1
[Note that some possible correct forms are: a g ( 1 ) = − or g (1 − k )
2
or g ( k ) − ] | M1
1 1
d g (1 ) t 2 = −
2 2 | M1A1
4d
t =
g(1−) | A1
(4)
7(b) | M1 Attempt to find the acceleration in terms of g and or g and k or g,
k and
M1 Complete method to find an equation in d, g, t andonly, condone a
sign error.
A1 Correct equation in d, g, t andonly
A1 Any equivalent form
--- 7(c) ---
7(c) | P or Q (or the system) would not move | B1
Accept any of T = mg, T m g , T m g , a = 0, a < 0, a0
F = T, F > T, F T , F > mg. Allow F replaced by R
N.B. Forces referred to must be clearly defined so
e.g. use of vague terms like ‘forward force’ , ‘opposite force’, ‘force to
the left or right’ is B0. | DB1
(2)
(13)
Notes for question 7
7(c) | B1 Correct statement. B0 if incorrect extras.
DB1 Correct reason
Allow column vectors throughout\includegraphics{figure_4}
A particle $P$ of mass $m$ is attached to one end of a light inextensible string. Another particle $Q$, also of mass $m$, is attached to the other end of the string. The string passes over a small smooth pulley which is fixed at the edge of a rough horizontal table. Particle $Q$ is held at rest on the table and particle $P$ hangs vertically below the pulley with the string taut, as shown in Figure 4.
The pulley, $P$ and $Q$ all lie in the same vertical plane.
The coefficient of friction between $Q$ and the table is $\mu$, where $\mu < 1$
Particle $Q$ is released from rest.
The tension in the string before $Q$ hits the pulley is $kmg$, where $k$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Find $k$ in terms of $\mu$. [7]
Given that $Q$ is initially a distance $d$ from the pulley,
\item find, in terms of $d$, $g$ and $\mu$, the time taken by $Q$, after release, to reach the pulley. [4]
\item Describe what would happen if $\mu \geqslant 1$, giving a reason for your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2022 Q7 [13]}}