Two identical steel cubes (masses 50g, side 1cm) 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=2xx10^(11)N//m^(2)`.

Explanation

Here, `m=50g=50xx10^(-3)kg`
side, `L=1cm=0.01m, upsilon=10cm//s=0.1m//s`
`Y=2xx10^(11)N//m^(2)`
Max. compression, `DeltaL=?`
Accroding to Hook's law,
`Y=(FL)/(ADeltaL) ` or `F=(YADeltaL)/(L)` …(i)
If `k` is compression constatn of the cube, then `F=kDeltaL`
Usin (i), `YA(DeltaL)/(L)=kDelta L`
`k=(YA)/(L)=(YL^(2))/(L)=YL` ...(ii)
Initial KE`=2xx(1)/(2)m upsilon^(2)=(50xx10^(-3))(0.1)^(2)=5xx10^(-4)J`
Final PE `=2xx(1)/(2)F(DeltaL)=2xx(1)/(2)(kDeltaL)(DeltaL)=2xx(1)/(2)k(DeltaL)^(2)=`Initial KE `=5xx10^(-4)`
`DeltaL=sqrt((5xx10^(-4))/(k))=sqrt((5xx10^(-4))/(YL))=sqrt((5xx10^(-4))/(2xx10^(11)xx0.01))=sqrt(2.5xx10^(-13))=5xx10^(-7)m`