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Physics · WORK, ENERGY AND POWER
हिन्दीA block of mass \( m \) moving with speed \( v \) collides with an uncompressed spring of stiffness \( k \) on a rough horizontal floor with coefficient of kinetic friction \( \mu \). If the maximum compression of the spring is \( x_m \), which equation correctly relates \( x_m \) to the system parameters?
Correct answer · Option 1
\( k x_m^2 + 2\mu m g x_m - m v^2 = 0 \)
Explanation
By work-energy theorem: \( \Delta K = W_{\text{net}} \implies 0 - \frac{1}{2}mv^2 = -\frac{1}{2}kx_m^2 - \mu mg x_m \implies \frac{1}{2}kx_m^2 + \mu mg x_m - \frac{1}{2}mv^2 = 0 \implies k x_m^2 + 2\mu mg x_m - mv^2 = 0 \).
