| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Projectile energy - basic KE/PE calculation |
| Difficulty | Moderate -0.8 This is a straightforward application of basic energy conservation principles with standard projectile motion. All parts require direct substitution into KE = ½mv² and PE = mgh formulas with minimal problem-solving. Part (d) is given away in the question stem. Easier than average A-level mechanics. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Kinetic energy = \(\frac{1}{2} \times 0.6 \times 15^2 = 67.5\) J | M1 A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(h = \frac{67.5}{0.6g} = 11.5\) m | M1 A1 A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Speed of ball is \(\sqrt{\frac{49.86}{\frac{1}{2} \times 0.6}} = 12.9\) m s\(^{-1}\) | M1 A1 m1 A1 | 4 marks |
| (d) eg ball is a particle, no air resistance, weight is the only force acting etc | E1 | 1 mark |
**(a)** Kinetic energy = $\frac{1}{2} \times 0.6 \times 15^2 = 67.5$ J | M1 A1 | 2 marks
**(b)** Using $mgh = \frac{1}{2}mv^2$:
$67.5 = 0.6 \times g \times h$
$h = \frac{67.5}{0.6g} = 11.5$ m | M1 A1 A1 | 3 marks
**(c)** When 3 m above ground level:
Change in PE is $0.6 \times g \times 3 = 17.64$ J
KE of ball is $67.5 - 17.64 = 49.86$ J
Speed of ball is $\sqrt{\frac{49.86}{\frac{1}{2} \times 0.6}} = 12.9$ m s$^{-1}$ | M1 A1 m1 A1 | 4 marks | No KE given: speed = 12.9 SC3; Dep on M1
**(d)** eg ball is a particle, no air resistance, weight is the only force acting etc | E1 | 1 mark
**Total: 10 marks**
---1 A ball is thrown vertically upwards from ground level with an initial speed of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ball has a mass of 0.6 kg . Assume that the only force acting on the ball after it is thrown is its weight.
\begin{enumerate}[label=(\alph*)]
\item Calculate the initial kinetic energy of the ball.
\item By using conservation of energy, find the maximum height above ground level reached by the ball.
\item By using conservation of energy, find the kinetic energy and the speed of the ball when it is at a height of 3 m above ground level.
\item State one modelling assumption which has been made.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2008 Q1 [10]}}