| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Newton's laws and connected particles |
| Type | Train with coupled trucks/carriages |
| Difficulty | Standard +0.3 This is a standard connected particles problem requiring straightforward application of Newton's second law to the system and individual bodies. Part (i) uses F=ma on the whole system, part (ii) repeats this with changed resistance, and part (iii) isolates one truck to find tension—all routine mechanics procedures with no novel insight required. Slightly above average difficulty due to multiple parts and careful bookkeeping of forces. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
**Question 8**
(i) $P - 1050 = 18000 \times 0.3$ [M1]
$P = 6450$ [A1]
(ii) New acceleration: $6450 - 2850 = 18000a$ [M1]
$a = 0.2$ [A1]
(iii) $6450 - 450 - T = 8000(0.2)$ [M1]
$T = 4400$ N [A1]
**Total: 6 marks**8 Two trucks, $S$ and $T$, of masses 8000 kg and 10000 kg respectively, are pulled along a straight, horizontal track by a constant, horizontal force of $P$ N. A resistive force of 600 N acts on $S$ and a resistive force of 450 N acts on $T$. The coupling between the trucks is light and horizontal (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{01bd6354-3514-4dad-901b-7ecbe155b2c7-5_213_1095_429_479}
The acceleration of the system is $0.3 \mathrm {~ms} ^ { - 2 }$ in the direction of the pulling force of magnitude $P$.\\
(i) Calculate the value of $P$.
Truck $S$ is now subjected to an extra resistive force of 1800 N . The pulling force, $P$, does not change.\\
(ii) Calculate the new acceleration of the trucks.\\
(iii) Calculate the force in the coupling between the trucks.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2016 Q8 [6]}}