| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | March |
| Marks | 9 |
| 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 connected particles problem with straightforward application of Newton's second law and SUVAT equations. Parts (a)-(c) involve routine force diagrams and kinematics with no conceptual challenges. Part (d) adds a conservation of momentum calculation, but all steps follow textbook procedures with clearly given data and no problem-solving insight required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \([T - 200 = 700 \times -12]\) Car: \(-T - 600 - F = 1600 \times -12\) System: \(-600 - 200 - F = 2300 \times -12\) | M1 | Apply Newton's 2nd law to the trailer or apply Newton's 2nd law to the car and to the system and eliminate the braking force \(F\) |
| Magnitude of \(T = 8200\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Car \([T - F - 600 = 1600 \times -12]\) or System \([-600 - 200 - F = 2300 \times -12]\) | M1 | Apply Newton's second law either to the car or to the system with braking force \(= F\) and use of *their* \(T\) from 6(a) |
| Braking force \(F = 26800\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \([v^2 = 22^2 + 2 \times -12 \times 17.5]\) | M1 | A complete method using constant acceleration equations which would lead to an equation for finding \(v\), using \(u = 22\), \(s = 17.5\) and \(a = -12\) |
| \(v = 8 \text{ ms}^{-1}\) | A1 | AG |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \([2300 \times 8 + m \times 0 = 2300 \times 2 + m \times 5]\) | M1 | For applying the conservation of momentum equation to the system of car, trailer and van, where \(m =\) mass of the van |
| A1 | Correct equation | |
| \(m = 2760\) kg | A1 |
## Question 6:
### Part 6(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $[T - 200 = 700 \times -12]$ Car: $-T - 600 - F = 1600 \times -12$ System: $-600 - 200 - F = 2300 \times -12$ | M1 | Apply Newton's 2nd law to the trailer or apply Newton's 2nd law to the car and to the system and eliminate the braking force $F$ |
| Magnitude of $T = 8200$ N | A1 | |
### Part 6(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Car $[T - F - 600 = 1600 \times -12]$ or System $[-600 - 200 - F = 2300 \times -12]$ | M1 | Apply Newton's second law either to the car or to the system with braking force $= F$ and use of *their* $T$ from **6(a)** |
| Braking force $F = 26800$ N | A1 | |
### Part 6(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $[v^2 = 22^2 + 2 \times -12 \times 17.5]$ | M1 | A complete method using constant acceleration equations which would lead to an equation for finding $v$, using $u = 22$, $s = 17.5$ and $a = -12$ |
| $v = 8 \text{ ms}^{-1}$ | A1 | AG |
### Part 6(d):
| Answer | Mark | Guidance |
|--------|------|----------|
| $[2300 \times 8 + m \times 0 = 2300 \times 2 + m \times 5]$ | M1 | For applying the conservation of momentum equation to the system of car, trailer and van, where $m =$ mass of the van |
| | A1 | Correct equation |
| $m = 2760$ kg | A1 | |
---6 On a straight horizontal test track, driverless vehicles (with no passengers) are being tested. A car of mass 1600 kg is towing a trailer of mass 700 kg along the track. The brakes are applied, resulting in a deceleration of $12 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The braking force acts on the car only. In addition to the braking force there are constant resistance forces of 600 N on the car and of 200 N on the trailer.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the force in the tow-bar.
\item Find the braking force.
\item At the instant when the brakes are applied, the car has speed $22 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. At this instant the car is 17.5 m away from a stationary van, which is directly in front of the car.
Show that the car hits the van at a speed of $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item After the collision, the van starts to move with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the car and trailer continue moving in the same direction with speed $2 \mathrm {~ms} ^ { - 1 }$.
Find the mass of the van.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q6 [9]}}