| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Connected particles via tow-bar on horizontal surface |
| Difficulty | Standard +0.3 This is a standard M2 connected particles problem with multiple parts requiring Newton's second law, power calculations, and resolving forces on an incline. While it involves several steps and careful bookkeeping of forces, each individual part uses routine mechanics techniques (F=ma, P=Fv, resolving parallel to slope) without requiring novel insight or complex problem-solving strategies. The 'show that' parts provide target answers to guide students, making it slightly easier than average. |
| Spec | 3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(F - 700 = 1650 \times 1.2\), \(F = 700 + 1980 = 2680 \text{ N}\) | M1 A1 A1 | |
| (b) \(F - 500 - T = 1100 \times 1.2\), \(T = 2180 - 1320 = 860 \text{ N}\) | M1 A1 A1 | |
| (c) \(P = 2680 \times 18 = 48.2 \text{ kW}\) | M1 A1 | |
| (d) \(48240 = 18(700 + 1650g\sin 6° + 1650a)\), \(a = 0.176 \text{ m s}^{-2}\) | M1 A1 A1 | |
| (e) For trailer, \(T - 200 - 550g\sin 6° = 550(0.176)\), \(T = 860 \text{ N}\) | M1 A1 A1 | Total: 14 marks |
(a) $F - 700 = 1650 \times 1.2$, $F = 700 + 1980 = 2680 \text{ N}$ | M1 A1 A1 |
(b) $F - 500 - T = 1100 \times 1.2$, $T = 2180 - 1320 = 860 \text{ N}$ | M1 A1 A1 |
(c) $P = 2680 \times 18 = 48.2 \text{ kW}$ | M1 A1 |
(d) $48240 = 18(700 + 1650g\sin 6° + 1650a)$, $a = 0.176 \text{ m s}^{-2}$ | M1 A1 A1 |
(e) For trailer, $T - 200 - 550g\sin 6° = 550(0.176)$, $T = 860 \text{ N}$ | M1 A1 A1 | Total: 14 marksA car, of mass 1100 kg, pulls a trailer of mass 550 kg along a straight horizontal road by means of a rigid tow-bar. The car is accelerating at 1.2 ms$^{-2}$ and the resistances to the motion of the car and trailer have magnitudes 500 N and 200 N respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that the driving force produced by the engine of the car is 2680 N. [3 marks]
\item Find the tension in the tow-bar between the car and the trailer. [3 marks]
\item Find the rate, in kW, at which the car's engine is working when the car is moving with speed 18 ms$^{-1}$. [2 marks]
\end{enumerate}
When the car is moving at 18 ms$^{-1}$ it starts to climb a straight hill which is inclined at $6°$ to the horizontal. If the car's engine continues to work at the same rate and the resistances to motion remain the same as previously,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find the acceleration of the car at the instant when it starts to climb the hill. [3 marks]
\item Show that tension in the tow-bar remains unchanged. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [14]}}