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.

Answer and Explanation:

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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...

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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.


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