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Why is the elongation in springs maximum when both the blocks have same velocity ? Pls Reply soon....
because they have zero velocity of approach
The system will have minimum kinetic energy.(Proved by writing a general equation of kinetic energy of system and differentiating it to find minima)
Therefore, maximum potential energy.
you can prove the situation mathematically but before that you must get a physical feeling of it.
see from the frame of one of the blocks. the velocities of the spring are definitely in the same line as the spring in the given situation. if in case the velocities are not equal then the relative velocity will not be zero. then in that case the other block will seem to go further or come closer as seen from the other causing an elongation or compression in the spring.
when the velocities are equal then there will be no further compression or elongation in the spring as the relative velocity will be zero. the second block will not seem to move towards or further from the first block.
now come to prove it mathematically.
see i guess in this situation there is no external force on the system of two blocks so in the entire process of motion the velocity of the center of mass will remain constant.
even when the velocities become equal they will be equal to the velocity of the center of mass of the system.
write the expression for the total energy. the total energy remains constant as there is no external force and/or work done by them is zero.
differentiate the equation and make the expression equal to zero. from this find the velocity. the velocities of the blocks will be same and equal to the velocity of the center of mass of the system.
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