Question #42335

A particle of mass $m = 3 \text{ kg}$ moving with an initial velocity $v_0 = 6 \text{ m/s}$ along the positive $x$-axis collides with a specialized energy-absorbing surface at $x = 0$. During the penetration ($x > 0$), the surface exerts a conservative restoring force derived from the potential $U(x) = A x^3$, where $A = 5 \text{ N/m}^2$. Additionally, the surface material exerts a non-conservative dissipative force of magnitude $F_d = B x^2$, where $B = 12 \text{ N/m}^2$, which always opposes the particle's velocity. What is the magnitude of the total impulse delivered by the particle to the surface during the entire collision process?