A diesel locomotive is pulling a heavy freight wagon along a level track using a horizontal steel coupling. The locomotive has a mass of 1500 kg1500\text{ kg}1500 kg. Its engine generates a constant tractive driving force of 1600 N1600\text{ N}1600 N, while encountering a constant resistive force of 350 N350\text{ N}350 N.
The wagon has a mass of 2500 kg2500\text{ kg}2500 kg and experiences a constant resistance to motion of R newtonsR\text{ newtons}R newtons.
The entire train maintains a constant acceleration of 0.15 m s−20.15\text{ m s}^{-2}0.15 m s−2.
(i) Calculate the value of RRR.
(ii) Determine the tension in the steel coupling.
Identify one physical assumption you have made regarding the steel coupling for your calculations in part (a).
While the train is moving at a velocity of 6 m s−16\text{ m s}^{-1}6 m s−1, the coupling fails at a specific location, KKK.
The wagon continues to travel, subject to the same resistance force RRR.
The locomotive continues forward but the driver applies brakes such that it comes to a standstill at a distance of 50 m50\text{ m}50 m from point KKK.
(i) By calculating the distance the wagon travels after the failure, determine if the wagon will collide with the stationary locomotive. Justify your conclusion.
(ii) Assuming the locomotive's tractive driving force had remained constant (ignoring the braking mentioned in part (c)(i)), describe how the locomotive's acceleration would change immediately after the coupling fails.
Practise Edexcel A Level Maths Applications of Forces with exam-style questions for A Level Maths. 47 questions covering Static Particles, Modelling with Statics, Friction and Static Particles, Static Rigid Bodies, Dynamics and Inclined Planes, and Connected Particles 2, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.