A linear spring of negligible mass requires a force of $18.0\,\text{N}$ to cause its length to increase by $1.0\,\text{cm}$. A sphere of mass $75.0\,\text{g}$ is then attached to one end of the spring. The distance between the center of the sphere $M$ and the other end $P$ of the un-stretched spring is $25.0\,\text{cm}$. Then the sphere begins rotating at constant speed in a horizontal circle around the center $P$. The distance between $P$ and $M$ increases to $26.5\,\text{cm}$.

Question

A linear spring of negligible mass requires a force of $18.0\,\text{N}$ to cause its length to increase by $1.0\,\text{cm}$. A sphere of mass $75.0\,\text{g}$ is then attached to one end of the spring. The distance between the center of the sphere $M$ and the other end $P$ of the un-stretched spring is $25.0\,\text{cm}$. Then the sphere begins rotating at constant speed in a horizontal circle around the center $P$. The distance between $P$ and $M$ increases to $26.5\,\text{cm}$.(a) Explain why the spring increases in length when the sphere is moving in a circle.
, (b) Determine the speed of the sphere.
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Jason · Accepted Answer

The spring stretches until its restoring force equals the required centripetal force, so the sphere moves outward and $\Delta x$ increases while rotating.
$9.77\,\text{m/s}$

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