Question

Could use some help getting started with this question. Thanks

Answer 1

The steel ingot shown in Fig. 2 has a mass of 1800 kg. It travels along the conveyor at a speed
v = 0.5 m/s when it collides with the nested spring assembly. Determine the maximum deflections in
each spring needed to stop the motion of the ingot, if kA = 5 kN/m and kB = 3 kN/m.

Answer 2

when it stops, the KE of the ingot will temporarily be stored as PE in the springs, and generally speaking we can say \(PE = \frac{1}{2}kx^2\)

here you will have different extensions (NB read: compressions) as the springs are staggered [we assume that the first spring will not stop the ingot in 0.1m but you can check that first if you like

thus we combine energy in the springs for a general extension x as \(PE = \frac{1}{2} \left[ k_a x^2 + k_b (x-0.1)^2\right]\)

hopefully \(x \lt 0.5\) or something is broken....