Problem — Spring compressed by a block

Problem

A spring of constant $k = 250\;\mathrm{N/m}$ is compressed horizontally by a block of mass $m = 0{,}50\;\mathrm{kg}$ travelling at $v = 3{,}0\;\mathrm{m/s}$. Neglecting friction, find the maximum compression of the spring.

Solution

At maximum compression the block is momentarily at rest: all the initial kinetic energy has been converted into elastic potential energy of the spring. $\frac{1}{2}\,m\,v^2 = \frac{1}{2}\,k\,x^2$ Solving for the compression $x$: $x = v\,\sqrt{\frac{m}{k}} = 3{,}0\;\mathrm{m/s}\cdot\sqrt{\frac{0{,}50\;\mathrm{kg}}{250\;\mathrm{N/m}}} = 3{,}0\cdot\sqrt{2{,}0\cdot 10^{-3}}\;\mathrm{m}$ $x = 3{,}0\cdot 0{,}0447\;\mathrm{m}$ $\ev{x \approx 0{,}14\;\mathrm{m}}$

Links

Topics: Work and energy Concepts: Elastic potential energy · Conservation of mechanical energy Skills: Conservation of energy Objects: Spring