Solving the Train and Spring Problem

[whereisccguys]

train and spring problem

problem: 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 go plowing 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 by being fully compressed, 4.2 feet. You assume that in order to keep the passengers safe when the spring stops the train, the maximum stopping acceleration of the train, caused by the spring, is g/2. You are not sure about the train's weight, so you make a guess that a train might have a mass of 0.5 million kilograms. For the purpose of getting your answer, you assume that all frictional forces are negligible.


What is the maximum train speed?

i thought it would be a simple problem of just setting the kinetic energy = to the work done by the force of the spring

1/2 m^2 V = Force*mass*distance
4.2ft=1.28m
g/2=4.9

and i got v = 3.542 m/s... but it's wrong... anyone know what i did wrong?

 

[Andrew Mason]

i thought it would be a simple problem of just setting the kinetic energy = to the work done by the force of the spring

You have to find the expression for the spring constant. Assume that the spring was designed so that the maximum stopping deceleration for this train is g/2 . Since the stopping acceleration depends on the mass of the train hitting it, one would have to assume then, that the average mass of trains hitting it would be .5 million kg.

From Hooke's Law, the maximum deceleration occurs at maximum compression. From that you can determine the k of the spring. Then use your energy approach to figure out the maximum v. However, you have to use the correct expression for spring energy. It is not force x mass x distance. (Note: it turns out that the answer is independent of mass).

I get 2.5m/s

AM

 

[whereisccguys]

ooo i understand... thanks a lot man