Chapter 14 - Kinetics of a Particle: Work and Energy - Section 14.6 - Conservation of Energy - Problems - Page 230: 96

$k=773N/m$

Work Step by Step

The required stiffness of the spring can be determined as follows: $T_1+V_1=T_2+V_2$ $\implies \frac{1}{2}mv_1^2+mgh_1+2\frac{1}{2}kx_1^2=\frac{1}{2}mv_2^2+mgh_2+2\frac{1}{2}kx_2^2$ We plug in the known values to obtain: $0+2(\frac{1}{2}k(2-1)^2)=0+2(\frac{1}{2}k(\sqrt{(0.5)^2+(2)^2}-1)^2)-20(9.81)(0.5)$ This simplifies to: $k=773N/m$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.