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A spring has a natural length of 28 cm. If a 23-N force is required to keep it stretched to a...

Question:

A spring has a natural length of 28 cm. If a 23-N force is required to keep it stretched to a length of 42 cm, how much work W is required to stretch it from 28 cm to 35 cm?

Work in Spring:

  • A spring is an energy storing device. When the length of a spring is changed from its original length by applying a force on it, there is a change in the potential energy of the spring. This energy is equal to the amount of external work done to it.

If a force F acts on a spring that changes the length of the spring by {eq}\Delta x {/eq}, then the amount of work required to stretch the spring is equal to the change in the potential energy of the spring and it is given as:

  • {eq}\begin{align} F&= k \Delta x \\[0.3cm] W &= \frac{1}{2} k (\Delta x )^2 \\[0.3cm] \end{align} {/eq}
  • In this equation, k is known as the spring constant.

Answer and Explanation:

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We have the following given data

{eq}\begin{align} \text{Narural Length:} ~~ x_0&= 28 ~~\rm{cm }\\[0.3cm] \text{Strectched Length:} ~~ x_1 &=42...

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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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