At the train station, you notice a large horizontal spring at the end of the track where the train comes in. This is a safety device to stop the train so that it will not plow through the station if the engineer misjudges the stopping distance. While waiting, you wonder what would be the fastest train that the spring could stop at its full compression, 3.0 ft. To keep the passengers safe when the train stops, you assume a maximum stopping acceleration of g/2. You also guess that a train weighs half a million lbs. For purpose of getting an estimate, you decide to assume that all frictional force are negligible.
(a) What is the algebraic expression for the speed of the fastest train that could be stopped by the spring in terms of the maximum compression of the spring (L), the weight of the train (W), and the gravitational acceleration (g)? [Note: Don't enter an equation like "x=blah". Just enter the "blah" part. All letters are capital except for "g".]
(b) What is the numerical value of the speed of the fastest train that could be stopped by the spring (make sure to include units and put a space between the number and the units)?
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