# A spring is stretched from its equilibrium position at x = 0 to a positive coordinate x_0. The...

## Question:

A spring is stretched from its equilibrium position at {eq}x = 0 {/eq} to a positive coordinate {eq}x_0 {/eq}. The force on the spring is {eq}F_0 {/eq} and it stores elastic potential energy {eq}PE_{s0} {/eq}. If the spring constant is doubled to {eq}2k_0 {/eq}, determine (a) the ratio of the new force to the original force, {eq}\frac{F_n}{F_0} {/eq}, and (b) the ratio of the new to the original elastic potential energy, {eq}\frac{PE_{sn}}{PE_{s0}} {/eq}.

## Elastic Element:

In reference to the elastic elements, the work being done on the element by load is a depending parameter upon the stretching or the contraction of the element and the modulus of elasticity of the element. This work gets stored as potential energy within the element.

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Given Data

• The initial displacement of the spring is: {eq}{x_o} {/eq}.
• The initial spring force is: {eq}{F_o} {/eq}.
• The initial potential energy...

Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.