A railcar with an overall mass of 75,000 kg traveling with a velocity υi is approaching a barrier equipped with a bumper constisting of a nonlinear spring whose force vs. compression law is given by Fs = βx3,where β = 640 × 106 N/m3 and x is the compression of the bumper.
Figure P3.29
Treating the system as a particle and assuming that the contact between the railcar and rails is frictionless, determine the maximum value of υi so that the compression of the bumper is limited to 20 cm.
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