| Exam Board | WJEC |
|---|---|
| Module | Further Unit 3 (Further Unit 3) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Maximum speed on incline vs horizontal |
| Difficulty | Standard +0.3 This is a standard mechanics problem applying P=Fv and F=ma with resistance forces. Part (a) is routine equilibrium, part (b) requires resolving forces on an incline and calculating acceleration from power, and part (c) is a straightforward conceptual question. All techniques are textbook applications with no novel insight required, making it slightly easier than average. |
| Spec | 6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product6.06a Variable force: dv/dt or v*dv/dx methods |
| Answer | Marks | Guidance |
|---|---|---|
| (a) At maximum speed \(F = R\) (N2L with \(a = 0\)) | M1 | Used |
| \(F = \frac{P}{v}\) | M1 | Used, si |
| \(2000 = \frac{80 \times 1000}{v}\) | ||
| \(v = 40\) (ms\(^{-1}\)) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| (b) \(F = \frac{0 \cdot 8 \times 80 \times 1000}{20} = 3200\) | B1 | si |
| N2L | M1 | All forces, dim. correct. \(F\) and \(R\) opposing |
| \(F - R - mg \sin \alpha = ma\) | A1 | Allow one error |
| \(F - 2000 - 1200g \times \frac{1}{20} = 1200a\) | A1 | FT candidates \(F\) |
| \(a = 0 \cdot 51\) (ms\(^{-2}\)) | A1 | cao |
| Answer | Marks |
|---|---|
| (c) Any valid reason. e.g. Resistance could vary with speed. | E1 |
**(a)** At maximum speed $F = R$ (N2L with $a = 0$) | M1 | Used
$F = \frac{P}{v}$ | M1 | Used, si
$2000 = \frac{80 \times 1000}{v}$ | |
$v = 40$ (ms$^{-1}$) | A1 | cao
**Subtotal: [3]**
**(b)** $F = \frac{0 \cdot 8 \times 80 \times 1000}{20} = 3200$ | B1 | si
N2L | M1 | All forces, dim. correct. $F$ and $R$ opposing
$F - R - mg \sin \alpha = ma$ | A1 | Allow one error
$F - 2000 - 1200g \times \frac{1}{20} = 1200a$ | A1 | FT candidates $F$
$a = 0 \cdot 51$ (ms$^{-2}$) | A1 | cao
**Subtotal: [5]**
**(c)** Any valid reason. e.g. Resistance could vary with speed. | E1 |
**Subtotal: [1]**
**Total for Question 4: 9**
---4. A car of mass 1200 kg has an engine that is capable of producing a maximum power of 80 kW . When in motion, the car experiences a constant resistive force of 2000 N .
\begin{enumerate}[label=(\alph*)]
\item Calculate the maximum possible speed of the car when travelling on a straight horizontal road.
\item The car travels up a slope inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 20 }$. If the car's engine is working at $80 \%$ capacity, calculate the acceleration of the car at the instant when its speed is $20 \mathrm {~ms} ^ { - 1 }$.
\item Explain why the assumption of a constant resistive force may be unrealistic.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 3 2019 Q4 [9]}}