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Suppose that 3 J of work is needed to stretch a spring from its natural length of 26 cm to a...

Question:

Suppose that 3 J of work is needed to stretch a spring from its natural length of 26 cm to a length of 44 cm.

(a) How much work is needed to stretch the spring from 34 cm to 36 cm? (Round your answer to two decimal places.)

(b) How far beyond its natural length will a force of 20 N keep the spring stretched? (Round your answer one decimal place.)

Elastic Potential Energy; Hooke's law:

The elastic potential energy is defined as the energy stored by a spring on stretching/compressing it from its natural length. It is expressed as:

{eq}E.P.E = \dfrac{ 1}{ 2 } k (\Delta x)^{2} {/eq}

And,

Hooke's law states that the restoring force applied by the spring, when it is stretched/compressed from its natural length, is directly proportional to the negative of the compression/elongation. Mathematically, it is expressed as:

{eq}F_{x} = - k \Delta x {/eq}

Where:

  • {eq}k {/eq} is the spring constant of the given spring.
  • {eq}\Delta x {/eq} is the compression/elongation in the spring from its natural length.

Answer and Explanation:

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Identify the given information in the problem:

  • The work done on the spring to stretch a spring from its natural length of {eq}26 \, \rm cm = 0.26...

See full answer below.


Learn more about this topic:

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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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