A block of mass m is projected straight upward by a strong spring whose stiffness is ks. When the block is a height y1 above
the floor, it is traveling upward at speed v1, and the spring is compressed an amount s1. A short time later the block is at
height y2, traveling upward at speed v2, and the spring is compressed an amount s2. In this discussion we'll use the Energy
Principle in the form Ef = Ei + W, where we assume that thermal transfer of energy (microscopic work) Q between the block
and the air is negligible. We can ignore the rest energies, which don't change, and the kinetic energy of the Earth, which
hardly changes.
I. System: Universe (block + spring + Earth)
For the system consisting of the block, the spring, and the Earth, write the Energy Principle in the update form Ef =
Ei + W.
II. System: Block + spring
For the system consisting of the block plus spring, write the Energy Principle in the update form Ef = Ei + W.
III. System: Block alone
For the system consisting of the block alone, write the Energy Principle in the update form Ef = Ei + W.