| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Coalescence collision |
| Difficulty | Moderate -0.3 This is a standard M1 momentum conservation problem with straightforward application of formulas. Students must apply conservation of momentum to find final velocity, determine direction from the sign, and calculate impulse using change in momentum. While it requires careful attention to signs and multiple steps (7 marks total), it involves only routine techniques with no novel problem-solving or geometric insight required—making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks |
|---|---|
| \(8mu - 3mu = 5mv\) | M1 A1 |
| \(v = u\) | A1 (3) |
| Answer | Marks |
|---|---|
| Original direction of motion of \(B\) o.e. | B1 (1) |
| Answer | Marks |
|---|---|
| For \(A\): \(I = m(u - (-3u))\) OR For \(B\): \(I = 4m(-u - (-2u))\) | M1 A1 |
| \(= 4mu\) | A1 (3) |
## Part (a)
$8mu - 3mu = 5mv$ | M1 A1 |
$v = u$ | A1 (3) |
## Part (b)
Original direction of motion of $B$ o.e. | B1 (1) |
## Part (c)
For $A$: $I = m(u - (-3u))$ OR For $B$: $I = 4m(-u - (-2u))$ | M1 A1 |
$= 4mu$ | A1 (3) |
**Notes for Question 1(a):**
M1 for attempt at CLM equation, with correct no. of terms, dimensionally correct. Allow consistent extra $g$'s and cancelled $m$'s and sign errors.
(M1 if they find the impulse on each particle and eliminate the impulse to give an equation – then use above criteria for their equation)
First A1 for a correct equation. $(3mu - 8mu = 5mv$ or $-5mv$ oe)
Second A1 for $u$ ($-u$ A0)
N.B. Allow $u$'s to be dropped or omitted in the equation if $u$ is inserted in answer at the end. (Full marks can be scored). However, if $u$ is not inserted then M0.
**Notes for Question 1(b):**
B1 for (original) direction of $B$ or opposite to original direction (of $A$) oe.
(B0 for 'left' or direction changed).
N.B. Must follow from $v = u$ or $-u$ obtained in (a).
**Notes for Question 1(c):**
M1 for attempt at impulse = difference in momenta, for either particle, (must be considering one particle) (M0 if $g$'s are included or if $m$ omitted or if mass doesn't match velocities used)
A1 for $\pm m(u - 3u)$ or $\pm 4m(-u - (-2u))$
A1 for $4mu$ cao ( - $4mu$ is A0) Allow change of sign at end to obtain magnitude.
---A railway truck $A$ of mass $m$ and a second railway truck $B$ of mass $4m$ are moving in opposite directions on a smooth straight horizontal track when they collide directly. Immediately before the collision the speed of truck $A$ is $3u$ and the speed of truck $B$ is $2u$. In the collision the trucks join together. Modelling the trucks as particles, find
\begin{enumerate}[label=(\alph*)]
\item the speed of $A$ immediately after the collision, [3]
\item the direction of motion of $A$ immediately after the collision, [1]
\item the magnitude of the impulse exerted by $A$ on $B$ in the collision. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q1 [7]}}