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\includegraphics[max width=\textwidth, alt={}, center]{8ee41313-b516-48cb-bc87-cd8e54245d28-4_314_997_267_577} A train of total mass 80000 kg consists of an engine \(E\) and two trucks \(A\) and \(B\). The engine \(E\) and truck \(A\) are connected by a rigid coupling \(X\), and trucks \(A\) and \(B\) are connected by another rigid coupling \(Y\). The couplings are light and horizontal. The train is moving along a straight horizontal track. The resistances to motion acting on \(E , A\) and \(B\) are \(10500 \mathrm {~N} , 3000 \mathrm {~N}\) and 1500 N respectively (see diagram).

1. By modelling the whole train as a single particle, show that it is decelerating when the driving force of the engine is less than 15000 N .
2. Show that, when the magnitude of the driving force is 35000 N , the acceleration of the train is \(0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
3. Hence find the mass of \(E\), given that the tension in the coupling \(X\) is 8500 N when the magnitude of the driving force is 35000 N . The driving force is replaced by a braking force of magnitude 15000 N acting on the engine. The force exerted by the coupling \(Y\) is zero.
4. Find the mass of \(B\).
5. Show that the coupling \(X\) exerts a forward force of magnitude 1500 N on the engine.