Yes, energy is transferred when you push a rock but don’t move it. While the rock remains stationary, the energy is converted into heat within your body and potentially into a small amount of potential energy within the rock itself. The rock experiences microscopic deformation due to the force applied, but this is not visible on a macroscopic scale.
Elaboration:
No External Displacement:
Since the rock doesn’t move, the energy is not transferred as kinetic energy (energy of motion).
Internal Energy (Heat):
The energy you expend in pushing the rock is transformed into heat within your muscles and body. This is why you feel tired and your body temperature may increase when exerting force without movement.
Potential Energy (Microscopic):
The rock does experience a very small amount of deformation. While this deformation is too small to be seen, the energy is stored as potential energy within the rock’s structure.
Law of Conservation of Energy:
The total energy of the system (you and the rock) remains constant, as energy is not lost but transformed.
Friction:
The energy is also used to overcome the static friction between the rock and the ground. This friction converts the energy into heat.