| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2009 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find acceleration on incline given power |
| Difficulty | Standard +0.3 This is a standard M2 power-force-acceleration problem requiring the formula P=Fv to find driving force, then resolving forces parallel to the incline (weight component, resistance, driving force) and applying F=ma. It involves multiple steps but uses routine techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03f Weight: W=mg6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(F = ma\) parallel to the slope | M1* | |
| \(T - 1500g\sin\theta - 650 = 1500a\) | A1 | |
| Tractive force: \(30000 = T \times 15\) | M1* | |
| \(a = \dfrac{\frac{30000}{15} - 1500(9.8)\left(\frac{1}{14}\right) - 650}{1500}\) | d*M1 | |
| \(\underline{0.2}\) (m s\(^{-2}\)) | A1 | |
| Total: [5] |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $F = ma$ parallel to the slope | M1* | |
| $T - 1500g\sin\theta - 650 = 1500a$ | A1 | |
| Tractive force: $30000 = T \times 15$ | M1* | |
| $a = \dfrac{\frac{30000}{15} - 1500(9.8)\left(\frac{1}{14}\right) - 650}{1500}$ | d*M1 | |
| $\underline{0.2}$ (m s$^{-2}$) | A1 | |
| **Total: [5]** | | |
---\begin{enumerate}
\item A car of mass 1500 kg is moving up a straight road, which is inclined at an angle $\theta$ to the horizontal, where $\sin \theta = \frac { 1 } { 14 }$. The resistance to the motion of the car from non-gravitational forces is constant and is modelled as a single constant force of magnitude 650 N . The car's engine is working at a rate of 30 kW .
\end{enumerate}
Find the acceleration of the car at the instant when its speed is $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
\hfill \mbox{\textit{Edexcel M2 2009 Q1 [5]}}