The figure represents an idealized one-dimensional structure of uniform mass ρ per unit le...

The figure represents an idealized one-dimensional structure of uniform mass ρ per unit length moving horizontally with a velocity v₀ when its front end collides with an immovable barrier and crushes. The force F required to initiate and maintain an accordionlike deformation is constant. Neglect the length b of the collapsed portion of the structure compared with the movement of s of the undeformed portion following the impact. The undeformed part may be viewed as a body of decreasing mass. Derive the differential equation which relates using Eq. 4/20 carefully. Check your expression by applying Eq. 4/6 to both parts together as a system of constant mass.