Hence the mass goes still through some distance.This happens till the opposing force equals the weight due to the mass.Thus the two forces are equal and opposite of one another and the mass is at rest only after the spring is compressed to some distance. If k is less the distance is greater and if k is more, distance is small.Same thing happens when you fall on a concrete or on grass.......
Initially the spring does not produce any opposing force. The opposing force is zero.
Hence the mass moves down through some distance, But corresponding to the distance depressed the spring exerts an upward force, = - kx . – kx will be less than the weight due to the mass . Hence the mass goes still through some distance.
This happens till the opposing force equals the weight due to the mass.
Thus the two forces are equal and opposite of one another and the mass is at rest only after the spring is compressed to some distance. If k is less the distance is greater and if k is more, distance is small.
Same thing happens when you fall on a concrete or on grass.
In the case of concrete the value of k for concrete is very high and the mass is stopped in a negligibly small distance. In the case of grass it is very less and the distance moved is greater till it is stopped by equal force .
since concrete is hard and not flexible, it wont dissipate the force it takes so force is concentrated in a single area. grass is much more "flexible" and therefore distributes the force to a certain area around it. to stop the momentum of the body, more time is required since the force on the man's feet is less than(because it is distributed) that of the concrete. Fnet*contact time = m(v-u).
