Based on Fig. P7.82, how much elastic potential energy is...

Based on Fig. P7.82, how much elastic potential energy is stored in the DNA when it is stretched $50 \mathrm{~nm}$ ? (a) $2.5 \times 10^{-19} \mathrm{~J}$; (b) $1.2 \times 10^{-19} \mathrm{~J}$; (c) $5.0 \times 10^{-12} \mathrm{~J}$; (d) $2.5 \times 10^{-12} \mathrm{~J}$.

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Key Concepts

Elastic Potential Energy

Elastic potential energy is the energy stored in a material or system when it is deformed, such as by stretching, compressing, or bending. This energy can be recovered when the material returns to its original shape, and the concept is central to understanding how forces and displacements cause energy changes in elastic systems.

Hooke's Law

Hooke's law states that, within the elastic limit, the force exerted by an elastic object is proportional to the displacement from its equilibrium position. This linear relationship (F = kx) is fundamental when analyzing how systems behave under applied forces, and it provides a foundation for calculating stored energy in elastic systems.

Energy Storage Formula in Elastic Systems

The energy stored in an elastic system can be calculated using the formula U = 1/2 k x^2, where k is the force constant or spring constant and x is the displacement from equilibrium. This formula quantifies the work done to deform the system and encapsulates the relationship between force, displacement, and energy storage in elastic materials.

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