Final answer:
Snapping a stick causes plastic deformation, and a ruler snaps with greater force due to its stiffness, causing more pain compared to a loose spring.
Step-by-step explanation:
When you snap a stick between your hands, breaking it into two pieces, you have caused plastic deformation. Plastic deformation is a change in shape under the application of a force where the object or material does not return to its original shape upon the removal of the force and instead retains a permanent deformation.
The reason it hurts more to be snapped with a ruler compared to a loose spring, despite equal displacement, relates to the stiffness of the systems. The ruler, being a stiffer system, exerts a greater force during the snap, leading to more pain. Human bones, similar to rulers, have a small elastic region and can sustain only a small amount of stress before fracturing, revealing that bones are quite brittle.
It is the stiffness of the ruler that results in a higher force for the same displacement, thus causing greater pain, unlike the less stiff, and therefore less painful, loose spring.