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Two boys struggled to move a tractor tire from flat on the floor to a position leaning against a wall. The sketch shows the tire initially 1) and finally 2).
What work did the boys do?
♦ Work, of the boys, accomplishes the energy change of the. Consequently we can take the tire (and Earth) as our system. We treat the tire as an extended body with its center of mass at its geometric center. The zero datum for potential energy will be the ground surface. We write the energy equation:
When we visualize the event we realize that the boys must stand the tire upright then roll it closer to the wall. Consequently the tire must attain a state intermediate to the two shown above. The states of interest are shown at the right.
Returning to Equation (1), there will be only one work effect; hence we drop the "Σ" of work. For the event between states 1) and 2), the kinetic energy is initially zero and finally zero but it will not be identically zero throughout the entire event. Since we have no way of knowing what it might be, we can only calculate the very least work of the boys.
The change of potential energy of Earth is zero. The potential energy change of the tire is proportional to the change of elevation of its center of mass. Calculation of the least work is as follows:
The boys, being small, lifted the tire slowly from the shop floor such that it never attained any kinetic energy while being lifted and tipped against the wall. So kinetic energies of the tire are zero. Whatever (the least) energy change as work by the boys to the tire equals the increase of potential energy of the tire. Mass times its change of elevation of its center of mass position, we can calculate its change of energy. Let's go that way.
The way of analysis is to display the idea, the energy equation. Then having faith, do all, everything easy to bring the idea, to focus it on the circumstance. We let the equation lead us to what we don't know.
b) The boys roll the tire next to a wall. Calculate the work. This requires work but not much if the boys work together. Boys fight sometimes. Who knows?
c) With the tire beside the wall, the boys let it fall from vertical to impact and rest against the wall (as shown). Assume the wall is perfectly rigid. Calculate the increase of internal energy of the tire.