Question

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 which is L=3 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.

Answer 1

Answer:

   v=2.13 m/s

Explanation:

Given that

L= 3 ft

We know that

1 ft = 0.3048 m

L=0.91 m

a= g/2

F= m a

F= m g/2 = K L

k= (mg)/(2L)

Now from energy conservation

Kinetic energy of train = potential energy of the spring

$\dfrac{1}{2}mv^2=\dfrac{1}{2}kL^2$

k= (mg)/(2L)

$\dfrac{1}{2}mv^2=\dfrac{1}{2}\times \dfrac{mg}{2L}L^2$

$v^2=\dfrac{g}{2}L$

$v=\sqrt{\dfrac{g}{2}L}$

By putting the values

$v=\sqrt{\dfrac{g}{2}L}$

$v=\sqrt{\dfrac{10\times 0.91}{2}}$     ( take g =10 m/s²)

v=2.13 m/s