A spring has a natural length of 20 cm. If a 30-N force is required to keep it stretched to a...

Question:

A spring has a natural length of 20 cm. If a 30-N force is required to keep it stretched to a length of 34 cm, how much work W is required to stretch it from 20 cm to 27 cm?

Spring

Spring is an elastic member that stores strain energy during compression and release the stored energy during the expansion. The force required to deform the spring by one unit is called the stiffness of the spring. Stiffness of the spring is measured in {eq}\text{N/m} {/eq} in SI units.

Answer and Explanation: 1


Let k is the stiffness of the spring

As per the statement, 30 N of force is needed to stretch a spring from 20 cm to 34 cm

By using Hooke's Law

$$\begin{align} F&=kx\\[0.3 cm] 30&=k \times (34-20)\\[0.3 cm] k&=\boxed{\color{blue}{2.142\ \text{N/cm}}} \end{align} $$

Work needed to strech the spring from 20 to 27 cm

$$\begin{align} W&=\dfrac{1}{2}\times k \times (\Delta x)^{2}\\[0.3 cm] &=\dfrac{1}{2}\times 2.142 \times (27-20)^{2}\\[0.3cm] &=\dfrac{1}{2}\times 2.142 \times 49\\[0.3 cm] &=\boxed{\color{blue}{52.479\ \text{N.cm}}} \end{align} $$


Learn more about this topic:

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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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