| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Vehicle pulling trailer - tension |
| Difficulty | Moderate -0.3 This is a straightforward M2 mechanics problem requiring standard application of Newton's second law and the power formula P=Fv. Part (a) involves finding total driving force using F=ma for the system, then calculating power. Part (b) requires isolating the caravan to find tension. All steps are routine with clear methodology and no conceptual subtlety, making it slightly easier than average. |
| Spec | 3.03k Connected particles: pulleys and equilibrium6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| \(F - 150 - 300 = 1500 \times 0.2\) | M1 | Needs total mass and both resistances. Condone sign errors |
| \(F = 750\) | A1 | Correct unsimplified equation |
| \(F = 750\) | A1 | |
| \(P = 750 \times 20 = 15000\) watts | M1 | Independent M. 20 x their driving force |
| A1 | ||
| (5) |
| Answer | Marks | Guidance |
|---|---|---|
| For caravan: \(T - 150 = 600 \times 0.2\) | M1 | Requires all forces acting on caravan. Condone sign error(s) |
| \(T = 270\) N | A1 | (2) |
| For car: \(F - T - 300 = 900 \times 0.2\) | M1 | Requires all forces acting on car. Condone sign error(s) |
| \(T = 270\) N | A1 | (2) |
| [7] |
| $F - 150 - 300 = 1500 \times 0.2$ | M1 | Needs total mass and both resistances. Condone sign errors |
| $F = 750$ | A1 | Correct unsimplified equation |
| $F = 750$ | A1 | |
| $P = 750 \times 20 = 15000$ watts | M1 | Independent M. 20 x their driving force |
| | A1 | |
| | (5) | |
**Or (b):**
Use their mass as a guide to which of these two alternatives is being used.
| For caravan: $T - 150 = 600 \times 0.2$ | M1 | Requires all forces acting on caravan. Condone sign error(s) |
| $T = 270$ N | A1 | (2) |
| For car: $F - T - 300 = 900 \times 0.2$ | M1 | Requires all forces acting on car. Condone sign error(s) |
| $T = 270$ N | A1 | (2) |
| | [7] | |
---A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod parallel to the road. The total resistance to motion of the car is modelled as having magnitude 300 N. The total resistance to motion of the caravan is modelled as having magnitude 150 N. At a given instant the car and the caravan are moving with speed 20 m s$^{-1}$ and acceleration 0.2 m s$^{-2}$.
\begin{enumerate}[label=(\alph*)]
\item Find the power being developed by the car's engine at this instant. [5]
\item Find the tension in the towbar at this instant. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q1 [7]}}