erobz said:
But you yourself don't fully believe this ( quoted from
https://www.physicsforums.com/threads/work-done-by-a-force-down-a-ramp.1052212/ )?
The only possible
external force acting on the car propelling the car up the hill is the force of static friction. I have found this problem in physics texts. Static Friction is the external force, and it is doing Work in the problems. The methodology clearly works, even though it is also clearly inconsistent.
It is often convenient to "zoom out", ignoring the details of an interaction and look at the bulk effects. We are back to the distinction between "real work" and "center of mass work"
Real work looks at the displacement of the material of the acted-on object at the point of contact under a particular force.
Center of mass work looks at the displacement of the center of mass of the acted-on object under a particular force. Or under the vector sum of all forces. With only one displacement to worry about, you are free to apply the distributive law and sum the forces before multiplying by displacement. ##\sum_i \vec{F_i} \cdot \Delta \vec{s} = \Delta \vec{s} \cdot \sum_i \vec{F_i}##
Zoom in (real work)...
If we are looking at the interface between tire and road, no work is being done. The two surfaces have zero relative motion (so no energy is being dissipated into heat) and, in addition, the surfaces have zero motion in our selected frame of reference (so no energy is being transferred as work between the mating surfaces).
Zoom out (center of mass work)...
But if we are looking at an abstract interface between motorbike and road, work
is being done. There is relative motion between the bike and road. So energy can either be dissipated or injected at the interface. As it turns out in the case at hand, energy is injected. The bike's engine produces the energy and the drive train transmits it into the interface (the rotating and driven wheel). The bike as a whole is in motion. We are zoomed out. We ignore the details of the engine and drive train and see an abstract force from the road on a moving bike. Non-zero work is done on the bike. Zero work is done on the road.
If you are treating the acted-on object as a either point-like or as a rigid, non-rotating blob effectively located at the center of mass then you are adopting the zoomed out point of view.
If you are paying attention to the inner details of the acted-on object such as rotation, vibration, waves, eddies and moving parts then you are adopting the zoomed in point of view.