| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Pile-driver or hammer impact |
| Difficulty | Standard +0.3 This is a straightforward multi-part mechanics problem requiring standard application of SUVAT equations, conservation of momentum, and work-energy principles. All steps are routine M1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(u=0\), \(s=0.5\), \(a=16\), use \(v^2 = u^2 + 2as\) | M1 | |
| \(v^2 = 0 + 2(16)(0.5) \therefore v = 4\) ms\(^{-1}\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Cons. of mom. \(12(4) = (12+4)V\) | M1 | |
| \(48 = 16V \therefore V = 3\) ms\(^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Eqn. of motion: \(16g - 1500 = 16a\) | M1 A1 | |
| \(\therefore a = -83.95\) | A1 | |
| Use with \(u=3\), \(v=0\) in \(v^2 = u^2 + 2as\) | M1 | |
| \(v^2 = 3^2 - 167.9s\) giving \(s = 0.054\) m \(= 5.4\) cm | M1 A1 | (11) |
## Question 5:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $u=0$, $s=0.5$, $a=16$, use $v^2 = u^2 + 2as$ | M1 | |
| $v^2 = 0 + 2(16)(0.5) \therefore v = 4$ ms$^{-1}$ | M1 A1 | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Cons. of mom. $12(4) = (12+4)V$ | M1 | |
| $48 = 16V \therefore V = 3$ ms$^{-1}$ | A1 | |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Eqn. of motion: $16g - 1500 = 16a$ | M1 A1 | |
| $\therefore a = -83.95$ | A1 | |
| Use with $u=3$, $v=0$ in $v^2 = u^2 + 2as$ | M1 | |
| $v^2 = 3^2 - 167.9s$ giving $s = 0.054$ m $= 5.4$ cm | M1 A1 | **(11)** |
---5. A sledgehammer of mass 12 kg is being used to drive a wooden post of mass 4 kg into the ground. A labourer moves the sledgehammer from rest at a point 0.5 m vertically above the post with constant acceleration $16 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ directed towards the post.
\begin{enumerate}[label=(\alph*)]
\item Find the velocity with which the sledgehammer hits the post.
When the sledgehammer hits the post, they both move together with common speed, $V$.
\item Show that $V = 3 \mathrm {~ms} ^ { - 1 }$.
As the sledgehammer hits the post, the labourer relaxes his grip and applies no further force. The sledgehammer and post are brought to rest by the action of a resistive force from the ground of magnitude 1500 N .
\item Find, in centimetres, the total distance that the sledgehammer and the post travel together before coming to rest.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [11]}}