160. In the figure below, an object of mass $m$ on a frictionless inclined surface has an initial velocity of $V_\circ = 4\,\dfrac{\text{m}}{\text{s}}$ and slides up the incline. If the maximum elastic potential energy of the spring equals $\frac{1}{8}$ of the initial kinetic energy of the object, what is the minimum length the spring compresses (in centimeters)? $$\left(\sin 37^\circ = 0.6,\ g = 10\,\frac{\text{m}}{\text{s}^2}\right)$$ [Figure: A mass $m$ on an inclined plane at angle $37^\circ$ with a spring of natural length $h = 85\,\text{cm}$ at the bottom, initial velocity $V_\circ$ directed up the incline.] \begin{flushright} (1) $20$ (2) $25$ (3) $30$ (4) $35$ \end{flushright} \rule{\textwidth}{0.4pt} \begin{flushright} Calculation Space \end{flushright} %% Page 11 Physics120-CPage 10
\textbf{160.} In the figure below, an object of mass $m$ on a frictionless inclined surface has an initial velocity of $V_\circ = 4\,\dfrac{\text{m}}{\text{s}}$ and slides up the incline. If the maximum elastic potential energy of the spring equals $\frac{1}{8}$ of the initial kinetic energy of the object, what is the minimum length the spring compresses (in centimeters)?
$$\left(\sin 37^\circ = 0.6,\ g = 10\,\frac{\text{m}}{\text{s}^2}\right)$$
\textit{[Figure: A mass $m$ on an inclined plane at angle $37^\circ$ with a spring of natural length $h = 85\,\text{cm}$ at the bottom, initial velocity $V_\circ$ directed up the incline.]}
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(1) $20$\\
(2) $25$\\
(3) $30$\\
(4) $35$
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\textbf{Calculation Space}
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