| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | October |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with friction after impact |
| Difficulty | Standard +0.3 This is a straightforward M1 collision problem requiring conservation of momentum (parts a,b) followed by a standard friction calculation using work-energy or SUVAT equations (part c). All steps are routine applications of standard mechanics formulas with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03v Motion on rough surface: including inclined planes6.03b Conservation of momentum: 1D two particles6.03d Conservation in 2D: vector momentum6.03i Coefficient of restitution: e |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2m \times 3u = 2mv + 4m \times 2u\) OR \(I = 4m \times 2u\) and \(-I = 2m(v-3u)\) AND add to eliminate \(I\) | M1A1 | Complete method giving equation in \(m\), \(u\) and \(v\) only, dimensionally correct, correct no. of terms, condone sign errors and consistent cancelled \(m\)'s or extra \(g\)'s |
| \(v = -u\) so speed is \(u\) | A1 | \(u\) must be positive |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Opposite to original direction, reversed, in opposite direction, direction \(QP\), opposite direction to \(Q\) | DB1 | Dependent on answer of \(+u\) or \(-u\) in (a). Direction changed is B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(R = 4mg\) | B1 | cao, seen anywhere e.g. on diagram |
| \(F = 4ma\) OR \(-Ft = 4m(0-2u)\) | M1 | Equation of motion (allow \(F\) for friction). OR Impulse-momentum equation |
| \(4mg\mu = 4ma\) | A1 | Correct equation with \(F\) substituted |
| \(0^2 = (2u)^2 - 2a\left(\dfrac{6u^2}{g}\right)\) OR \(\dfrac{6u^2}{g} = \dfrac{(0+2u)}{2}t\) | M1A1 | Use of suvat for equation in \(u\) and \(a\) only. OR impulse-momentum in \(u\) and \(t\) only. Equations must be consistent to earn both A marks |
| \(\mu = \dfrac{1}{3}\) correctly obtained | A1 | Accept 0.33 or better |
# Question 2:
## Part 2(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2m \times 3u = 2mv + 4m \times 2u$ OR $I = 4m \times 2u$ and $-I = 2m(v-3u)$ AND add to eliminate $I$ | M1A1 | Complete method giving equation in $m$, $u$ and $v$ only, dimensionally correct, correct no. of terms, condone sign errors and consistent cancelled $m$'s or extra $g$'s |
| $v = -u$ so speed is $u$ | A1 | $u$ must be positive |
## Part 2(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Opposite to original direction, reversed, in opposite direction, direction $QP$, opposite direction to $Q$ | DB1 | Dependent on answer of $+u$ or $-u$ in (a). Direction changed is B0 |
## Part 2(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $R = 4mg$ | B1 | cao, seen anywhere e.g. on diagram |
| $F = 4ma$ OR $-Ft = 4m(0-2u)$ | M1 | Equation of motion (allow $F$ for friction). OR Impulse-momentum equation |
| $4mg\mu = 4ma$ | A1 | Correct equation with $F$ substituted |
| $0^2 = (2u)^2 - 2a\left(\dfrac{6u^2}{g}\right)$ OR $\dfrac{6u^2}{g} = \dfrac{(0+2u)}{2}t$ | M1A1 | Use of suvat for equation in $u$ and $a$ only. OR impulse-momentum in $u$ and $t$ only. Equations must be consistent to earn both A marks |
| $\mu = \dfrac{1}{3}$ correctly obtained | A1 | Accept 0.33 or better |
---2. A particle $P$ of mass $2 m$ is moving on a rough horizontal plane when it collides directly with a particle $Q$ of mass $4 m$ which is at rest on the plane. The speed of $P$ immediately before the collision is $3 u$. The speed of $Q$ immediately after the collision is $2 u$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $u$, the speed of $P$ immediately after the collision.
\item State clearly the direction of motion of $P$ immediately after the collision.
Following the collision, $Q$ comes to rest after travelling a distance $\frac { 6 u ^ { 2 } } { g }$ along the plane. The coefficient of friction between $Q$ and the plane is $\mu$.
\item Find the value of $\mu$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2021 Q2 [10]}}