# A student places her 380 g physics book on a frictionless table. She pushes the book against a...

## Question:

A student places her 380 g physics book on a frictionless table. She pushes the book against a spring, compressing the spring by 7.80 cm, and then releases the book. What is the book's speed as it slides away? The spring constant is 1500 N/m.

## Strain Energy:

When an object is dropped on a spring, the object compresses the spring. The magnitude of the energy stored in the spring due to that compression is called the strain energy.

We are given the following data:

• Mass of book, {eq}m=380\ \rm g {/eq}
• Force constant of spring, {eq}k=1500\ \rm N/m {/eq}
• Compression of the spring, {eq}X=7.8\ \rm cm {/eq}

We are asked to calculate the compression of the spring; we can do so using the principle of conservation of energy. The kinetic energy of the book is equal to the energy stored in the spring due to compression. If (V) is the velocity of the spring, we have:

{eq}\begin{align} K.E&=E_{s}\\[0.3 cm] \dfrac{1}{2} mV^{2}&=\dfrac{1}{2}kx^{2}\\[0.3 cm] 380\times10^{-3}\ \rm kg\times V^{2}&=1500\ \rm N/m\times (7.80\times10^{-2}\ \rm m)^{2}\\[0.3 cm] V&=\boxed{4.90\ \rm m/s}\\[0.3 cm] \end{align} {/eq}

Practice Applying Spring Constant Formulas

from

Chapter 17 / Lesson 11
3.1K

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.