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

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}