| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Pile-driver or hammer impact |
| Difficulty | Moderate -0.8 This is a standard M1 mechanics question testing routine application of SUVAT equations, conservation of momentum in an inelastic collision, and impulse-momentum theorem. All parts follow textbook methods with no problem-solving insight required—part (a) is given as 'show that', parts (b-d) are direct one-step or two-step calculations using standard formulas. Easier than average A-level due to its highly structured, procedural nature. |
| Spec | 3.02h Motion under gravity: vector form6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) "\(v^2 = u^2 + 2as\)": \(V^2 = 2 \cdot 9.8 \cdot 1.6\) \(\Rightarrow V = 5.6 \text{ m s}^{-1}\) | M1, A1 | 2 marks |
| (b) \(78 \cdot 5.6 = 84 \cdot v\) \(\Rightarrow v = 5.2 \text{ m s}^{-1}\) | M1 A1, A1 | 3 marks |
| (c) \(84 \cdot 5.2 = F \cdot 0.06 - 84g \cdot 0.06\) \(\Rightarrow F = 8103.2 \text{ N}\) | M1 A1 A1, A1 | 4 marks |
| (d) "\(F = ma\)": \(8103.2 - 84g = 84a \Rightarrow a = 86.67\) "\(v^2 = u^2 + 2as\)": \(5.2^2 = 2 \cdot 86.67 \cdot s\) \(\Rightarrow s \approx 0.156 \text{ m, or } 0.16 \text{ m to } 2 \text{ s.f.}\) | M1 A1, M1, A1 | 4 marks |
**(a)** "$v^2 = u^2 + 2as$": $V^2 = 2 \cdot 9.8 \cdot 1.6$ $\Rightarrow V = 5.6 \text{ m s}^{-1}$ | M1, A1 | 2 marks
**(b)** $78 \cdot 5.6 = 84 \cdot v$ $\Rightarrow v = 5.2 \text{ m s}^{-1}$ | M1 A1, A1 | 3 marks
**(c)** $84 \cdot 5.2 = F \cdot 0.06 - 84g \cdot 0.06$ $\Rightarrow F = 8103.2 \text{ N}$ | M1 A1 A1, A1 | 4 marks
**(d)** "$F = ma$": $8103.2 - 84g = 84a \Rightarrow a = 86.67$ "$v^2 = u^2 + 2as$": $5.2^2 = 2 \cdot 86.67 \cdot s$ $\Rightarrow s \approx 0.156 \text{ m, or } 0.16 \text{ m to } 2 \text{ s.f.}$ | M1 A1, M1, A1 | 4 marks
---A post is driven into the ground by means of a blow from a pile-driver. The pile-driver falls from rest from a height of $1.6$ m above the top of the post.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of the pile-driver just before it hits the post is $5.6$ m s$^{-1}$. [2]
\end{enumerate}
The post has mass $6$ kg and the pile-driver has mass $78$ kg. When the pile-driver hits the top of the post, it is assumed that the there is no rebound and that both then move together with the same speed.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the speed of the pile-driver and the post immediately after the pile-driver has hit the post. [3]
\end{enumerate}
The post is brought to rest by the action of a resistive force from the ground acting for $0.06$ s.
By modelling this force as constant throughout this time,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the magnitude of the resistive force, [4]
\item find, to 2 significant figures, the distance travelled by the post and the pile-driver before they come to rest. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [13]}}