A 1-m spring is compressed to half its original length. What is the potential energy stored within the spring? (Note: k = 40 N/m)

Question

A 1-m spring is compressed to half its original length.  What is the potential energy stored within the spring?  (Note:  k = 40 N/m)

Quizplus · Accepted Answer

11ecba2d_131d_fe5e_a3bf_014e4036a092_MD0008_00 Potential energy refers to a form of stored energy that depends on the spatial position or configuration of objects. Essentially, potential energy is the capacity of an object within a system to do work in the future based on some work completed on it in the past. In mechanical systems, potential energy accumulates because of the work performed by a force applied over some distance. The type of potential energy stored within an object is related to the type of force that previously performed work on the object. For example, gravitational potential energy accumulates when the height of an object increases because a force must act against gravity to raise the object. Similarly, stretching or compressing a spring away from its equilibrium point (ie, its position at rest) increases its elastic potential energy (U_el) because displacing a spring requires doing work against the elastic forces resisting displacement. The potential energy stored within a compressed or stretched spring explains why harmonic oscillations take place when the spring is released after being compressed or stretched. The magnitude of potential energy stored within a compressed or stretched spring is a function of spring displacement (x) and the spring constant (k), a measure of the relative elasticity (stiffness) of the spring: 11ecba2d_131d_fe5f_a3bf_83243d783fcb_MD0008_00 In this question, a spring with a length of 1 m is compressed to 0.5 m by a force, which gives the spring a displacement of 0.5 m. The spring constant is 40 N/m, which indicates that maintaining a displacement of 1 m away from the equilibrium position of the spring requires 40 N of force. Consequently, the magnitude of potential energy stored within the spring from a 0.5-m displacement is: 11ecba2d_131e_2570_a3bf_95959616b7e4_MD0008_00 11ecba2d_131e_2571_a3bf_d3a2a44bcda4_MD0008_00 11ecba2d_131e_2572_a3bf_cfddadd09c18_MD0008_00 Therefore, compressing the 1-m spring to half its original length imparts a potential energy into the spring equivalent to 5.0 J (Choice B). Educational objective: Elastic potential energy refers to the potential energy of springs and other elastic objects. Elastic potential energy increases following the application of a stretching or compressing force that displaces a spring from its equilibrium position.

A 1-M Spring Is Compressed to Half Its Original Length