For the system below with bars AB and CD made of a material

For the system below with bars AB and CD made of a material of Young\'s Modulus E, obtain the maximum deformation of each bar if the block of mass X slugs has an initial velocity, v_0.

Solution

KE of the block = (1/2)*X*v₀²

Elastic Energy stored in each bar = F²L / (2AE).........where F is the force on each bar

By energy conservation,

(1/2)*X*v₀² = 2*F²L / (2AE)

F = sqrt [X * v₀² * AE / (2L)]

Deformation of each bar = FL / AE

= sqrt [X * v₀² * L / (2AE)]