# Suppose that 4 J of work is needed to stretch a spring from its natural length of 36 cm to a...

## Question:

Suppose that 4 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 45 cm.

(a) How much work is needed to stretch the spring from 41 cm to 43 cm? _____J

(b) How far beyond its natural length will a force of 40 N keep the spring stretched?_____cm

## Energy Stored in Spring

When a force is applied to a spring, it gets stretched from its original length and stores some energy into it. The amount of energy stored in the spring during its stretching is called the strain energy.

Let k is the stiffness of the spring

As per the statement,4 J of work is needed to stretch a spring from 36 cm to 45 cm

The change in length of the spring is {eq}\Delta \text{x}=45-36=9\ \text{cm} {/eq}

By using Hooke's Law

\begin{align} W&=\dfrac{1}{2}\times k \times (\Delta x)^{2}\\[0.3 cm] 4&=\dfrac{1}{2}\times k \times (9)^{2}\\[0.3cm] 4&=\dfrac{1}{2}\times k \times81\\[0.3 cm] k&=0.0987\ \text{N/cm} \end{align}

(a) Work needed to strech the spring from 41 to 43 cm

\begin{align} W&=\dfrac{1}{2}\times k \times (\Delta x)^{2}\\[0.3 cm] &=\dfrac{1}{2}\times 0.0987 \times (43-41)^{2}\\[0.3cm] &=\dfrac{1}{2}\times k \times81\\[0.3 cm] &=\boxed{\color{blue}{0.7896\ \text{J}}} \end{align}

(b) Distance beyond the natural length that a force of 40 N keep the spring streched

By using Hooke's Law

\begin{align} F&=kx\\[0.3 cm] 40&=0.0987\times x\\[0.3 cm] x&=\boxed{\color{blue}{405.2\ \text{cm}}} \end{align}

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

from

Chapter 4 / Lesson 19
201K

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.