| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Average power over journey |
| Difficulty | Standard +0.3 This is a straightforward M2 work-energy question requiring standard formulas (mass flow rate from volume, GPE and KE calculations) with clear given values. The multi-step nature and unit conversions add slight complexity, but it follows a predictable template with no conceptual challenges or novel problem-solving required. |
| Spec | 6.02a Work done: concept and definition6.02d Mechanical energy: KE and PE concepts |
| Answer | Marks |
|---|---|
| X-sect. area of pipe \(= \pi r^2 = \pi(0.05)^2\) | M1 A1 |
| mass of water per second \(= 6 \times 0.0025\pi \times 1000 = 15\pi\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| energy gained \(= \frac{1}{2}mv^2 + mgh = \frac{15}{8}\pi(6)^2 + (150\pi \times 9.8 \times 12)\) | M2 A1 | |
| \(= 6390 J = 6.39 \text{ kJ (3sf)}\) | A1 | (8) |
**Part (a):**
X-sect. area of pipe $= \pi r^2 = \pi(0.05)^2$ | M1 A1 |
mass of water per second $= 6 \times 0.0025\pi \times 1000 = 15\pi$ | M1 A1 |
**Part (b):**
energy gained $= \frac{1}{2}mv^2 + mgh = \frac{15}{8}\pi(6)^2 + (150\pi \times 9.8 \times 12)$ | M2 A1 |
$= 6390 J = 6.39 \text{ kJ (3sf)}$ | A1 | (8)
---2. A pump raises water from a well 12 metres below the ground and ejects the water through a pipe of diameter 10 cm at a speed of $6 \mathrm {~ms} ^ { - 1 }$.
Given that the mass of $1 \mathrm {~m} ^ { 3 }$ of water is 1000 kg ,
\begin{enumerate}[label=(\alph*)]
\item find, in terms of $\pi$, the mass of water discharged by the pipe every second,
\item find in kJ , correct to 3 significant figures, the total mechanical energy gained by the water per second.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q2 [8]}}