| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2019 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find steady/maximum speed given power |
| Difficulty | Standard +0.3 This is a standard Further Mechanics question on power, requiring application of P=Fv and F=ma to find resistance forces, then using P=Rv at maximum speed. Part (a) uses constant resistance, part (b) proportional resistance (both routine calculations), and part (c) asks for basic model comparison. Slightly above average difficulty due to being Further Maths content and requiring careful handling of two models, but follows a well-established template with no novel insight required. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{60000}{10} - R = 1500 \times 3.3\) | M1 | \(= 4950\) |
| \(R = 1050\) | A1 | May be \(-1050\) |
| \(\frac{60000}{v} = 1050\) | M1 | |
| Greatest speed is \(57.1 \text{ ms}^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{60000}{10} - k \times 10 = 1500 \times 3.3\) | M1 | Or \(1050 = 10k\) |
| \(k = 105\) | A1 | |
| \(\frac{60000}{v} = 105v\) | M1 | |
| \(v^2 = 571.4\ldots\) | A1 | |
| \(v = 23.9 \text{ ms}^{-1}\) | A1 | Must be positive |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The constant resistance model does not seem to be very accurate | B1ft | B1 for each of two correct statements about the models; If commenting on accuracy of (a), must emphasise that (a) is very inaccurate; Do not allow: model (a) is not very effective / Neither model is accurate / (a) and (b) are not very accurate |
| The refined (linear) model gives a much more accurate answer than the constant resistance model | B1ft | Clear comparison between accuracy of the two models; must emphasise (b) is fairly accurate or considerably more accurate than (a); Do not allow: model (b) is more accurate than (a) / (b) is not accurate / resistance is proportional to speed or to speed² |
## Question 3:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{60000}{10} - R = 1500 \times 3.3$ | M1 | $= 4950$ |
| $R = 1050$ | A1 | May be $-1050$ |
| $\frac{60000}{v} = 1050$ | M1 | |
| Greatest speed is $57.1 \text{ ms}^{-1}$ | A1 | |
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{60000}{10} - k \times 10 = 1500 \times 3.3$ | M1 | Or $1050 = 10k$ |
| $k = 105$ | A1 | |
| $\frac{60000}{v} = 105v$ | M1 | |
| $v^2 = 571.4\ldots$ | A1 | |
| $v = 23.9 \text{ ms}^{-1}$ | A1 | Must be positive |
### Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| The constant resistance model does not seem to be very accurate | B1ft | B1 for each of two correct statements about the models; If commenting on accuracy of (a), must emphasise that (a) is very inaccurate; Do not allow: model (a) is not very effective / Neither model is accurate / (a) and (b) are not very accurate |
| The refined (linear) model gives a much more accurate answer than the constant resistance model | B1ft | Clear comparison between accuracy of the two models; must emphasise (b) is fairly accurate or considerably more accurate than (a); Do not allow: model (b) is more accurate than (a) / (b) is not accurate / resistance is proportional to speed or to speed² |
---3 A car of mass 1500 kg has an engine with maximum power 60 kW . When the car is travelling at $10 \mathrm {~ms} ^ { - 1 }$ along a straight horizontal road using maximum power, its acceleration is $3.3 \mathrm {~ms} ^ { - 2 }$.
In an initial model of the motion of the car it is assumed that the resistance to motion is constant.
\begin{enumerate}[label=(\alph*)]
\item Using this initial model, find the greatest possible steady speed of the car along the road.
In a refined model the resistance to motion is assumed to be proportional to the speed of the car.
\item Using this refined model, find the greatest possible steady speed of the car along the road.
The greatest possible steady speed of the car on the road is measured and found to be $21.6 \mathrm {~ms} ^ { - 1 }$.
\item Explain what this value means about the models used in parts (a) and (b).
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS 2019 Q3 [11]}}