A2 June 2022 Q2
2.
A van of mass 600 kg is moving up a straight road which is inclined at an angle \(\alpha\) to the horizontal, where \(\sin\alpha = \dfrac{1}{15}\). The van is towing a trailer of mass 150 kg. The van is attached to the trailer by a towbar which is parallel to the direction of motion of the van and the trailer, as shown in Figure 1.
The resistance to the motion of the van from non-gravitational forces is modelled as a constant force of magnitude 200 N.
The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude 100 N.
The towbar is modelled as a light rod.
The engine of the van is working at a constant rate of 12 kW.
Find the tension in the towbar at the instant when the speed of the van is \(9\ \text{m s}^{-1}\) (8)
| Scheme | Marks | AO |
|---|---|---|
 | ||
| Equation of motion for the system or for the van | M1 | 3.3 |
| \(F - (100 + 200) - (150 + 600)g\sin\alpha = (150 + 600)a\) or \(F - 200 - T - 600g\sin\alpha = 600a\) | A1 A1 | 1.1b 1.1b |
| Equation of motion for the trailer | M1 | 3.1b |
| \(T - 100 - 150g\sin\alpha = 150a\) | A1 | 1.1b |
| Use of \(F = \dfrac{12000}{9}\) | M1 | 3.4 |
| Solve for \(T\) | M1 | 1.1b |
| \(T = 307\ (310)\ (\text{N})\) | A1 | 2.2a |
| (8 marks) |
Notes
M1: Need all terms and no extras (the inclusion of \(+T\) \(-T\) is not an error). Dimensionally correct. Condone sign errors and sin/cos confusion
Must have non-zero acceleration and include the driving force
A1: Unsimplified equation in \(F\) or their \(F\) (and \(T\) if relevant) with at most one error
A1: Correct unsimplified equation in \(F\) or their \(F\) (and \(T\) if relevant)
M1: Need all terms. Dimensionally correct. Condone sign errors and sin/cos confusion
Or a second equation of motion involving the driving force.
A1: Correct unsimplified equation (in \(T\) and / or \(F\) or their \(F\) if relevant)
M1: Use of \(P = Fv\) seen or implied.
M1: Complete method to find \(T\) \(\big(\text{FYI}: a = 0.72(4)\big)\)
A1: Tension correct to 3 sf or 2 sf
A fractional answer \(\left(\dfrac{920}{3}\right)\) is not acceptable because this result follows the use of \(g = 9.8\)