Final answer:
The higher the spring constant (k), the greater the elastic potential energy (PEs) of an object for a given displacement from an equilibrium position, because a stiffer spring requires more force to deform.
Step-by-step explanation:
The spring constant, which is denoted by the symbol k, directly affects the elastic potential energy stored in an object when it is displaced from its equilibrium position. Using the formula PEs = ½ kx², we can see that the potential energy is proportional to the square of the displacement (x) and also to the spring constant (k). Therefore, the higher the spring constant, the stiffer the spring, and thus the greater the elastic potential energy for a given displacement.
The correct statement is: The higher the spring constant, the greater the elastic potential energy.
This statement is true because a stiffer spring (with a higher spring constant) requires more force to compress or stretch it, which results in more work done on the spring and hence more energy stored in the form of elastic potential energy.