| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Connected particles via tow-bar on horizontal surface |
| Difficulty | Moderate -0.8 This is a straightforward two-body mechanics problem requiring only Newton's second law (F=ma) applied twice. Students identify forces, apply F=ma to each object separately, and solve simple linear equations. It's easier than average as it involves standard M1 technique with no conceptual challenges, though the two-part structure and careful force identification prevent it from being trivial. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Net force on trailer is \(+/-(700 - R_T)\) | B1 | For applying Newton's second law to the trailer with 2 terms on LHS (no vertical forces) |
| \(700 - R_T = 600 \times 0.8\) Resistance is 220N | M1 A1ft A1 | ft cv(+/-(700 - R_T)) |
| (ii) \(2100 - 700 - R_C = 1100 \times 0.8\) or \(2100 - (R_C + 220) = (1100 + 600)x 0.8\) Resistance is 520N | M1 A1ft A1 | For applying Newton's second law to the car or to the whole, with a \(=+/-\) 0.8 (no vertical forces) ft cv(220) |
(i) Net force on trailer is $+/-(700 - R_T)$ | B1 | For applying Newton's second law to the trailer with 2 terms on LHS (no vertical forces)
$700 - R_T = 600 \times 0.8$ Resistance is 220N | M1 A1ft A1 | ft cv(+/-(700 - R_T))
(ii) $2100 - 700 - R_C = 1100 \times 0.8$ or $2100 - (R_C + 220) = (1100 + 600)x 0.8$ Resistance is 520N | M1 A1ft A1 | For applying Newton's second law to the car or to the whole, with a $=+/-$ 0.8 (no vertical forces) ft cv(220)
---A trailer of mass 600 kg is attached to a car of mass 1100 kg by a light rigid horizontal tow-bar. The car and trailer are travelling along a horizontal straight road with acceleration $0.8 \text{ m s}^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Given that the force exerted on the trailer by the tow-bar is 700 N, find the resistance to motion of the trailer. [4]
\item Given also that the driving force of the car is 2100 N, find the resistance to motion of the car. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 2007 Q1 [7]}}