A 4.8 × 105 kg subway train is brought to a stop from a speed of 0.55 m/s in 0.42 m by a large spring bumper at the end of its track.

Question

 What is the force constant k of the spring in N/m? 

Answer 1

All of the kinetic energy of the train must be converted to elastic potential energy of the spring.

mv²/2 = kx²/2

k = mv²/x²

Plug in

m = 4.8 x 10⁵ kg

v = 0.55 m/s

x = 0.42 m

and get k in N/m.