| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Average power over journey |
| Difficulty | Moderate -0.8 This is a straightforward application of standard energy formulas (PE = mgh, KE = ½mv², Power = Energy/time) with all values given directly. It requires only substitution into memorized formulas with no problem-solving, making it easier than average for A-level mechanics. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\Delta PE = mgh = 400 \times 9.8 \times 8 = 31360\) J | B1 | Accept \(31\,400\) J using \(g = 9.81\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(KE = \frac{1}{2} \times 400 \times 2^2 = 800\) J | B1 | Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Total energy \(= 31360 + 800 = 32160\) J | M1 | Sum of PE and KE gains |
| Power \(= \frac{32160}{60} = 536\) W | A1 | Divide by 60 seconds |
# Question 3:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\Delta PE = mgh = 400 \times 9.8 \times 8 = 31360$ J | B1 | Accept $31\,400$ J using $g = 9.81$ |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $KE = \frac{1}{2} \times 400 \times 2^2 = 800$ J | B1 | Correct answer |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Total energy $= 31360 + 800 = 32160$ J | M1 | Sum of PE and KE gains |
| Power $= \frac{32160}{60} = 536$ W | A1 | Divide by 60 seconds |3 A pump is being used to empty a flooded basement.\\
In one minute, 400 litres of water are pumped out of the basement.\\
The water is raised 8 metres and is ejected through a pipe at a speed of $2 \mathrm {~ms} ^ { - 1 }$.\\
The mass of 400 litres of water is 400 kg .
\begin{enumerate}[label=(\alph*)]
\item Calculate the gain in potential energy of the 400 litres of water.
\item Calculate the gain in kinetic energy of the 400 litres of water.
\item Hence calculate the power of the pump, giving your answer in watts.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2011 Q3 [4]}}