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  • Two identical steel cubes collide head-on face to face with a speed of 10 cm/s each.

Two identical steel cubes(mass 50g, sides 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 = 2 \times 10^{11} N/m^{2}.

Answers (1)

The kinetic energies of the cubes when they collide, converts into potential energy.

From the hooks law we know that, stress α strain

Y = stress/strain 

Y=\frac{FL}{A\Delta L}

F=\frac{ AY \Delta L}{L} = LY\Delta L

Work done = F. \Delta L = LY. \Delta L^{2}

Kinetic energy

= 2\left (\frac{1}{2} m v^{2} \right ) = 0.05 \times 0.1 \times 0.1 = 5 \times 10 ^{-4} J

As WD=KE,

LY. \Delta L^{2} = 5 \times 10 ^{-4}

\Delta L =\sqrt{ 25 \times 0.0001} = 5 \times 10 ^{-7} m

Posted by

infoexpert24

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