3 Fig. 7 illustrates a train with a locomotive, L, pulling two trucks, A and B.
The locomotive has mass 90 tonnes and is subject to a resistance force of 2000 N .
Each of the trucks \(A\) and \(B\) has mass 30 tonnes and is subject to a resistance force of \(500 N\).
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\caption{Fig. 7}
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Initially the train is travelling along a straight horizontal track. The locomotive is exerting a driving force of 12000 N .
- Find the acceleration of the train.
- Find the tension in the coupling between trucks A and B .
When the train is travelling at \(10 \mathrm {~ms} ^ { - 1 }\), a fault occurs with truck A and the resistance to its motion changes from 500 N to 5000 N .
The driver reduces the driving force to zero and allows the train to slow down under the resistance forces and come to a stop.
- Find the distance the train travels while slowing down and coming to a stop.
Find also the force in the coupling between trucks A and B while the train is slowing down, and state whether it is a tension or a thrust.
The fault in truck A is repaired so that the resistance to its motion is again 500 N . The train continues and comes to a place where the track goes up a uniform slope at an angle of \(\alpha ^ { \circ }\) to the horizontal.
- When the train is on the slope, it travels at uniform speed. The driving force remains at 12000 N . Find the value of \(\alpha\).
- Show that the force in the coupling between trucks A and B has the same value that it had in part (ii).