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A block of mass \( M \) slides on a frictionless surface with an initial speed of \( v_{0} \). On top of block is a small box of mass \( m \). The
\( \mathrm{P} \) coefficients of friction between box and block are \( \mu_{s} \) and \( \mu_{k} \). The sliding block encounters an ideal spring with force constant \( k \).
W Answer following questions.
What is maximum value of \( k \) for which it remains true that box does not slide?
(1) \( \left(\frac{\mu_{s} g}{v_{0}}\right)^{2} \frac{M}{(M+m)} \)
(2) \( \left(\frac{\mu_{s} g}{v_{0}}\right)^{2} M \)
(3) \( \left(\frac{\mu_{s} g}{2 v_{0}}\right)^{2} \frac{(M+m)^{2}}{M} \)
(4) \( \left(\frac{\mu_{s} g}{v_{0}}\right)^{2}(M+m) \)
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