train usually stops in such a position that the couplings between trucks are taut (since the buffers, which are compressed during braking, push the trucks apart and tauten the couplings). Therefore the locomotive, if it is to move the train forward, must overcome the static friction of all the trucks at once. But if it pushes the train backwards, first it pushes only the first truck and in doing this it has to overcome the static friction of one truck. Once the truck has started moving static friction
112 SOLUTIONS
gives place to the sliding friction of the ball bearings in the wheel axles and the rolling friction of the wheels on the rails. These forces are considerably less than that of static friction. Therefore when it pushes the first truck and the second truck backwards, the locomotive is able to overcome the second truck's static friction and so on. After the whole train has started to move backwards and the buffers of all the trucks are compressed, the locomotive changes to forward gear. Then, as it tautens the coupling of the first truck, it is overcoming at first the static friction of only the first truck, then that of only the second, and so on, until the whole train is moving. The compressed buffers between the trucks also help this.