Answer to Question #167853 in Physics for clar

Question

You attach your 4.55 - kg Physics for Engineers book to a horizontal spring (k = 629 N/m). You then pull the book to a distance of 7.6 cm and released it from rest. If the coefficient of kinetic friction between your book and the surface is 0.31, calculate the block's speed as it passes through its original position.

Answer 1

$kx^2/2=mv^2/2+W_{fr}$

$kx^2/2=mv^2/2+\mu mgx\to$

$v=\sqrt{2(kx^2/2-\mu mgx)/m}=\sqrt{2(629\cdot 0.076^2/2-0.31\cdot4.55\cdot9.8\cdot 0.076)/4.55}=$

$=0.58\ (m/s)$ . Answer