Question

A block of a mass m kg moving with kinetic energy 3J on a smooth horizontal surface hits the free end of a spring, whose other end is attached to a rigid wall as shown in the figure. If restoring force applied by the spring is given by $f\left(x\right)=-2x-x^3(N{)}_b$ Then the maximum compression in the spring approximately

• A. 2.20m
• B. 1.51m
• C. 1.41m
• D. 1.67m

Answer 1

The correct option is C 1.41m

$U={\int }_0^T(-2x-x^3)dx=x^2+\frac{x^4}{4}$ Since there is no loss energy , so

$\frac{x^4}{4}+x^2=E_1=\frac{1}{2}m{v}^2=3\Rightarrow x^4+4x^2-12=0\Rightarrow x^2=\frac{+4\pm \sqrt{16+48}}{2}=\frac{-4\pm 8}{2}=-6,+2$

$\Rightarrow x=\sqrt{2}$