Question

A block of 4 kg is free to move on horizontal frictionless surface. Initially left spring is relaxed. Now block is shifted to left by $20cm$ and released. Both the springs are identical, $K=800N/m$ and shaded part is rough. Find maximum compression in spring on the right ($\mu =0.8$)

• A. 20 cm
• B. 12 cm
• C. 15 cm
• D. 10 cm

Answer 1

The correct option is C 15 cm

Loss in stored energy = Work done by non conservative force
$\frac{1}{2}k{x}^2-\left(\mu mg\right)\times d=\frac{1}{2}k{x^{{}^{\prime }}}^2$
$\frac{1}{2}\times \left(800\right)(0.2{)}^2-0.8\times 4\times 10d=\frac{1}{2}\times (800){x^{{}^{\prime }}}^2$
$x^{{}^{\prime }}=\sqrt{\frac{9}{400}}$
$x=\frac{3}{20}=15cm$