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 + Wext, 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, which of the following equations correctly represents the energy principle in the form Ef = Ei + Wext?
(1/2)mv22 - (1/2)kss22 = (1/2)mv12 - (1/2)kss12 - mg(y2-y1)
(1/2)mv22 + (1/2)kss22 = (1/2)mv12 + (1/2)kss12 - mg(y2-y1)
(1/2)mv22 - mgy2 + (1/2)kss22 = (1/2)mv12 - mgy1 + (1/2)kss12
(1/2)mv22 = (1/2)mv12 - (1/2)ks(s22 - s12) - mg(y2-y1)
(1/2)mv22 = (1/2)mv12 + (1/2)ks(s22 - s12) + mg(y2-y1)
(1/2)mv22 + mgy2 + (1/2)kss22 = (1/2)mv12 + mgy1 + (1/2)kss12
II. System: block + spring For the system consisting of the block plus spring, which of the following equations correctly represents the energy principle in the form Ef = Ei + Wext?
(1/2)mv22 + mgy2 + (1/2)kss22 = (1/2)mv12 + mgy1 + (1/2)kss12
(1/2)mv22 - (1/2)kss22 = (1/2)mv12 - (1/2)kss12 - mg(y2-y1)
(1/2)mv22 = (1/2)mv12 - (1/2)ks(s22 - s12) - mg(y2-y1)
(1/2)mv22 = (1/2)mv12 + (1/2)ks(s22 - s12) + mg(y2-y1)
(1/2)mv22 + (1/2)kss22 = (1/2)mv12 + (1/2)kss12 - mg(y2-y1)
(1/2)mv22 - mgy2 + (1/2)kss22 = (1/2)mv12 - mgy1 + (1/2)kss12
III. System: block alone For the system consisting of the block alone, which of the following equations correctly represents the energy principle in the form Ef = Ei + Wext?
(1/2)mv22 - mgy2 + (1/2)kss22 = (1/2)mv12 - mgy1 + (1/2)kss12
(1/2)mv22 + mgy2 + (1/2)kss22 = (1/2)mv12 + mgy1 + (1/2)kss12
(1/2)mv22 + (1/2)kss22 = (1/2)mv12 + (1/2)kss12 - mg(y2-y1)
(1/2)mv22 = (1/2)mv12 + (1/2)ks(s22 - s12) + mg(y2-y1)
(1/2)mv22 - (1/2)kss22 = (1/2)mv12 - (1/2)kss12 - mg(y2-y1)
(1/2)mv22 = (1/2)mv12 - (1/2)ks(s22 - s12) - mg(y2-y1)