Question

a mass of 200 kg travels down a frictionless roller coaster from a height of 50 m. When it reaches the level ground (height 0 m) it encounters an unstretched horizontal spring with spring constant 10,000 N/m. As the mass comes to a rest how far does it compress the spring?

Answer 1

just before touching the spring Kinetic energy = potential energy at top = 200*9.8*50

on touching the spring this energy gets converted into potential energy of spring

so 0.5*10000*x^2 = 200*9.8*50

=> x = 4.43 m