| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Year | 2018 |
| Session | September |
| Marks | 5 |
| Topic | Power and driving force |
| Difficulty | Moderate -0.3 This is a straightforward mechanics problem requiring application of F=ma, resolving forces on an incline, and using P=Fv. All steps are standard textbook procedures with no novel insight required. The multi-part structure and need to handle component resolution makes it slightly more involved than trivial recall, but it remains below average difficulty for A-level Further Maths students who are expected to handle mechanics fluently. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| \(D = 140 - 850g\sin 7° = 850 \times 0.4\) | M1, M1, A1 | N11, 4 terms, component of mg; \(D = 1495\); \(17942.06\) W |
| \(P = D \times 12\) oe soi | M1 | |
| awrt 17900 (or 17.9kW) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{17942.06}{v} = 140 + 850g\sin 7°\) | M1 | FT their 17942.06 |
| \(v = 15.5\) so the constant speed is \(15.5 \text{ m s}^{-1}\) | A1 |
## (i)
$D = 140 - 850g\sin 7° = 850 \times 0.4$ | M1, M1, A1 | N11, 4 terms, component of mg; $D = 1495$; $17942.06$ W
$P = D \times 12$ oe soi | M1 |
awrt 17900 (or 17.9kW) | A1 |
## (ii)
$\frac{17942.06}{v} = 140 + 850g\sin 7°$ | M1 | FT their 17942.06
$v = 15.5$ so the constant speed is $15.5 \text{ m s}^{-1}$ | A1 |
---A car of mass 850 kg is being driven uphill along a straight road inclined at $7°$ to the horizontal. The resistance to motion is modelled as a constant force of magnitude 140 N. At a certain instant the car's speed is $12 \text{ms}^{-1}$ and its acceleration is $0.4 \text{ms}^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Calculate the power of the car's engine at this instant. [3]
\item Find the constant speed at which the car could travel up the hill with the engine generating this power. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics 2018 Q1 [5]}}