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The energy that is stored in an object when it is either stretched or compressed is referred to as elastic potential energy. This form of energy arises as a result of the deformation of the object; for example, when you stretch a rubber band or compress a spring, work is done to deform those materials. This deformation causes the molecules within the material to store energy. When the object returns to its original shape, the stored energy is released. This is a key characteristic of elastic potential energy, making it distinct from other forms of energy.
Kinetic energy involves the energy of motion, which does not apply to an object that is merely stretched or compressed. Gravitational potential energy relates to an object's position in a gravitational field, like an object held at a height, while thermal energy is associated with the internal energy of a substance due to the kinetic energy of its molecules. Therefore, elastic potential energy is the correct term for the stored energy in a stretched or compressed object.