A 100 kg point mass falls from H = 10 mm onto a massless elastic bar of area 100 mm², length 1 m and Young’s modulus 100 GPa, fixed at its base as shown. With g = 10 m/s², find maximum bar compression in mm.
Bar stiffness is $k=AE/L=10^{-4}(10^{11})/1=10^7$ N/m. During compression $\delta$, the mass descends a total $H+\delta$. Energy balance is $mg(H+\delta)=k\delta^2/2$. The positive solution is $\delta=[mg+\sqrt{(mg)^2+2kmgH}]/k$. Substituting $mg=1000$ N and $H=0.01$ m gives $\delta=0.0015177$ m = 1.518 mm, within the accepted interval 1.50–1.52 mm.
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