| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2001 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Car towing trailer, horizontal |
| Difficulty | Moderate -0.3 This is a standard M1 connected particles question requiring Newton's second law applied to a two-body system. Part (a) involves straightforward F=ma on horizontal ground, part (b) requires considering forces on one vehicle separately to find tension, and part (c) extends to an inclined plane with given sin α. All steps follow routine procedures taught in M1 with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-part structure and inclusion of an inclined plane component. |
| Spec | 3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| \(3200a = 2320 - 800 - 240\) | M1 A1 | |
| \(a = 0.4 \text{ ms}^{-2}\) | A1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(1200a = T - 240\) | M1 A2 \(-1\) e.e. | |
| \(\Rightarrow T = 720 \text{ N}\) | A1 | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(3200a' = 2320 - 1040 - 3200g \cdot \frac{1}{20}\) (4 terms) | M1 A2 \(-1\) e.e. | |
| \(a' = -0.09 \text{ ms}^{-2}\) | M1 | |
| \(\Rightarrow\) magnitude \(0.09 \text{ ms}^{-2}\), speed decreasing | A1 A1 | (6 marks) Total: 13 |
## Question 6:
### Part (a) — Car + Van:
$3200a = 2320 - 800 - 240$ | M1 A1 |
$a = 0.4 \text{ ms}^{-2}$ | A1 | (3 marks)
### Part (b) — Car alone:
$1200a = T - 240$ | M1 A2 $-1$ e.e. |
$\Rightarrow T = 720 \text{ N}$ | A1 | (4 marks)
**OR Van:** $2000a = 2320 - 800 - T \Rightarrow T = 720 \text{ N}$
NB: If equations used for car and van alone, allow M1 A2 for one equation involving $T$, then M1 A1 for second equation, then A1 A1 for $a$ and $T$.
### Part (c):
$3200a' = 2320 - 1040 - 3200g \cdot \frac{1}{20}$ (4 terms) | M1 A2 $-1$ e.e. |
$a' = -0.09 \text{ ms}^{-2}$ | M1 |
$\Rightarrow$ magnitude $0.09 \text{ ms}^{-2}$, speed decreasing | A1 A1 | (6 marks) **Total: 13**
---6. A breakdown van of mass 2000 kg is towing a car of mass 1200 kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800 N and 240 N respectively. There is a constant driving force acting on the van of 2320 N . Find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the acceleration of the van and the car,
\item the tension in the tow bar.
The two vehicles come to a hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 20 }$. The driving force and the resistances to the motion are unchanged.
\item Find the magnitude of the acceleration of the van and the car as they move up the hill and state whether their speed increases or decreases.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2001 Q6 [13]}}