Q. 444.5( 2 Votes )

A block of mass m moving at a speed u compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.

Answer :

The spring constant is calculated as


Given


The mass of the block is given as “m”, and the speed of the block is “u” and distance is “x”.


Formula Used


Using the conversation of energy, we equate the energies of spring compression and potential energy of the mass of the block, the formula of the energy stored in spring compression is



And the energy stored in the block is formulated as



where


The value of spring constant is denoted as “k”, the compression distance is “x”, the mass of the block is given as “m”, v is the velocity of the block.


Explanation


The velocity of the block given as “u” and after compression it becomes , making the initial kinetic energy as



The total energy or the initial kinetic energy is equal to final kinetic energy and the spring compression energy.





Therefore, the spring constant is calculated as


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