| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.3 This is a standard M1 momentum/impulse question requiring straightforward application of conservation of momentum and impulse-momentum theorem. Part (a) involves routine algebraic manipulation with given masses and velocities, while part (b) is a simple substitution. The question is slightly easier than average as it's a textbook collision problem with no conceptual surprises or complex problem-solving required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | cons. of mom.: \(3mu - 2mu = 2mv\) (dir° of B after coll. taken as +ve) | M2 |
| \(mu = 2mv \therefore v = \frac{1}{2}u\) | A1 | |
| hence, speed of B halved and change of sign means dir° has reversed | B1 | |
| (b) | impulse = Δ mom. i.e. for A, \(9m = 0 - (-3mu)\) | M2 |
| \(9m = 3mu \therefore u = 3\) | A1 | (7) |
(a) | cons. of mom.: $3mu - 2mu = 2mv$ (dir° of B after coll. taken as +ve) | M2 |
| $mu = 2mv \therefore v = \frac{1}{2}u$ | A1 |
| hence, speed of B halved and change of sign means dir° has reversed | B1 |
(b) | impulse = Δ mom. i.e. for A, $9m = 0 - (-3mu)$ | M2 |
| $9m = 3mu \therefore u = 3$ | A1 | (7) |A particle $A$ of mass $3m$ is moving along a straight line with constant speed $u$ m s$^{-1}$. It collides with a particle $B$ of mass $2m$ moving at the same speed but in the opposite direction. As a result of the collision, $A$ is brought to rest.
\begin{enumerate}[label=(\alph*)]
\item Show that, after the collision, $B$ has changed its direction of motion and that its speed has been halved. [4 marks]
\end{enumerate}
Given that the magnitude of the impulse exerted by $A$ on $B$ is $9m$ Ns,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $u$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [7]}}