Using work energy theorem, consider the gravitational potential energy at its lowest position of compression to be zero, because change in kinetic energy is 0 then;
mgx-(kx)²/2 =0 where m is mass of object, g is acceleration due to gravity, k is spring contant and x is the compression on the spring.
mgx=(kx)²/2
x=2mg/k----------------compression when velocity of object is Zero
But ΔK.E =-1/2mv²⇒kx²=mv² -----------where v is velocity of the object and K.E is kinetic energy
So if kx²=mv² then
v=x *√(k/m) ----------------where v=0
Doubling v will multiply the x *√(k/m) by 2 making x₂ twice x₁
To make sure that we have enough resourses to sustain ourselves. You see, if we use up, say, all water on earth, then obviously we won't have any more and we'll die.
