Moderate -0.3 This is a straightforward connected particles problem requiring application of Newton's second law to two bodies separately. Students must identify forces correctly and set up two simultaneous equations (F = ma for car and trailer), then solve algebraically. While it involves multiple steps and careful bookkeeping of forces, it follows a standard template with no conceptual surprises, making it slightly easier than average.
2 A car of mass 1500 kg is towing a trailer of mass \(m \mathrm {~kg}\) along a straight horizontal road. The car and the trailer are connected by a tow-bar which is horizontal, light and rigid. There is a resistance force of \(F \mathrm {~N}\) on the car and a resistance force of 200 N on the trailer. The driving force of the car's engine is 3200 N , the acceleration of the car is \(1.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and the tension in the tow-bar is 300 N .
Find the value of \(m\) and the value of \(F\).
Must have correct number of terms. Allow sign errors. Must use 300 and 1.25, not \(T\) and \(a\).
Trailer: \(300 - 200 = m \times 1.25\) or Car: \(3200 - F - 300 = 1500 \times 1.25\) or System: \(3200 - F - 200 = (1500 + m) \times 1.25\)
A1
Any 2 equations. Third equation could be with *their* \(m\) substituted if found already.
Solve for \(m\) or \(F\)
M1
Must get to '\(m =\)' or '\(F =\)'. Must have correct number of terms. Allow sign errors. Can be implied by correct answers.
\(m = 80\) and \(F = 1025\)
A1
4
**Question 2:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to use Newton's second law | M1 | Must have correct number of terms. Allow sign errors. Must use 300 and 1.25, not $T$ and $a$. |
| Trailer: $300 - 200 = m \times 1.25$ or Car: $3200 - F - 300 = 1500 \times 1.25$ or System: $3200 - F - 200 = (1500 + m) \times 1.25$ | A1 | Any 2 equations. Third equation could be with *their* $m$ substituted if found already. |
| Solve for $m$ or $F$ | M1 | Must get to '$m =$' or '$F =$'. Must have correct number of terms. Allow sign errors. Can be implied by correct answers. |
| $m = 80$ and $F = 1025$ | A1 | |
| | **4** | |
2 A car of mass 1500 kg is towing a trailer of mass $m \mathrm {~kg}$ along a straight horizontal road. The car and the trailer are connected by a tow-bar which is horizontal, light and rigid. There is a resistance force of $F \mathrm {~N}$ on the car and a resistance force of 200 N on the trailer. The driving force of the car's engine is 3200 N , the acceleration of the car is $1.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and the tension in the tow-bar is 300 N .
Find the value of $m$ and the value of $F$.\\
\hfill \mbox{\textit{CAIE M1 2023 Q2 [4]}}