Question

A 4.50 ✕ 10⁵ kg subway train is brought to a stop from a speed of 0.500 m/s in 0.300 m by a large spring bumper at the end of its track. What is the force constant k of the spring?

Answer 1

m = mass of the train = 4.50 x 10⁵ kg

v_i = initial speed of the train = 0.500 m/s

v_f = final speed of the train = 0 m/s

x = compression of the spring = 0.3 m

k = force constant of the spring

using conservation of energy

initial kinetic energy of the train = spring potential energy due to compression + final kinetic energy of train

(0.5) m v_i² = (0.5) m v_f² + (0.5) k x²

inserting the values

(4.50 x 10⁵) (0.500)² = (4.50 x 10⁵) (0)² + k (0.3)²

k = 1.25 x 10⁶ N/m