June 2024 Paper 1 Q2
2 A car of mass 1400 kg pulls a trailer of mass 400 kg along a straight horizontal road. The engine of the car produces a driving force of 6000 N. A resistance of 800 N acts on the car. A resistance of 300 N acts on the trailer. The tow-bar between the car and the trailer is light and horizontal.
| Scheme | Marks | AO |
|---|---|---|
 | B1 B1 | 1.1 1.1 |
| [2] |
Notes
B1: Driving force and common tension correct and labelled. Allow \(T_1\) and \(T_2\) if later seen equated. Ignore any vertical forces shown. Also allow for common thrust.
B1: Both resistances correct and labelled and no extra horizontal forces
| Scheme | Marks | AO |
|---|---|---|
| N2L for system \(6000 - 800 - 300 = 1800a\) | M1 M1 | 1.1a 1.1a |
| \(a = 2.72\ \text{m s}^{-2}\) (to 3 s.f.) | A1 | 1.1 |
| [3] |
Notes
M1: Attempt to find resultant horizontal force. All forces included and no extras Allow sign errors.
M1: Attempts N2L equation with their total mass and their resultant. Do not allow for weight used instead of mass.
A1: cao
Alternative solution
| Scheme | Marks | AO |
|---|---|---|
| N2L for car \(6000 - 800 - T = 1400a\) N2L for trailer \(T - 300 = 400a\) | M1 | |
| Add equations to give | M1 | |
| \(a = 2.72\ \text{m s}^{-2}\) (to 3 s.f.) | A1 |
M1: Attempt at N2L for at least one part of the system Do not allow for weight used instead of mass. Allow sign errors. All forces included and no extras
(Use the mass to determine which part of the system considered)
M1: Attempt to eliminate \(T\) from their two equations
A1: cao