And rolls downhill on tracks from a mine. At the end of the tracks, 21 m lower vertically, is a horizontally situated spring with constant 3.3 × 105 N/m. The acceleration of gravity is 9.8 m/s 2 . Ignore friction. How much is the spring compressed in stopping the ore car?

The spring is compressed 7.15 meters.                      

Explanation:

Let us assume that the mass of the car, m = 41000 kg                  

Position of the tracks, h = 21 m

Spring constant of the spring, acceleration due to gravity,

Let the spring is compressed by a distance of x in stopping the ore car. In this case, the potential energy is balanced by the increase in spring potential energy such that :

So, the spring is compressed 7.15 meters.