Q.47 Two identical steel cubes (masses 50g, side 1 cm) collide head-on face to face with a speed of 10 cm/s each. Find the maximum compression of each. Young's modulus for steel =Y=2×1011N/m2.

Hint: All KE will be converted to elastic potential energy.
Step 1: Find the Initial kinetic energy of the system of two cubes.

Let

m=50g=50×103kg Side =L=1cm=0.01m Speed =v=10cm/s=0.1m/s Young's modulus =Y=2×1011N/m2 Maximum compression ΔL=?

In this case, all KE will be converted to PE
By Hooke's law,    
where A is the surface area and L is the length of the side of the cube If k is spring or compression constant. then

InitialKE=2×12mv2=5×104J
Step2:Findtheexpressionofelasticenergystoredinthesystemoftwocube.
ByHook'slaw
FA=YΔLL
whereAisthesurfaceareaandListhelengthofthesideofthecube
Ifkisspringconstant,then
 force F=kΔL
k=YAL=YL
FinalPE=2×12k(ΔL)2
Step3:FindmaximumcompressionofeachofthecubesbyequatingtotalkineticenergywithtotalPE.
ΔL=KEk=KEγL=5×1042×1011×0.1=1.58×107m[PE=KE]