A block of mass m moving at a speed v compres | vedclass

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(C) According to the Work-Energy Theorem,the work done by the spring force is equal to the change in kinetic energy of the block.The work done by the

Vedclass · Accepted Answer

$\frac{15mv^2}{16x^2}$

Vedclass · Answer

(C) According to the Work-Energy Theorem,the work done by the spring force is equal to the change in kinetic energy of the block.The work done by the spring force is $W_s = -\frac{1}{2}kx^2$.The change in kinetic energy is $\Delta K = K_f - K_i = \frac{1}{2}m(v_f^2 - v_i^2)$.Given the final speed $v_f = \frac{v}{4}$ and initial speed $v_i = v$,we have:$-\frac{1}{2}kx^2 = \frac{1}{2}m\left(\left(\frac{v}{4}\right)^2 - v^2\right)$$-\frac{1}{2}kx^2 = \frac{1}{2}m\left(\frac{v^2}{16} - v^2\right)$$-\frac{1}{2}kx^2 = \frac{1}{2}m\left(-\frac{15v^2}{16}\right)$$kx^2 = \frac{15mv^2}{16}$$k = \frac{15mv^2}{16x^2}$

$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

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