Cycloid

A small stone with a mass of $m=$  g is stuck in a tire. The radius of the tire is $R=$  m. The stone follows a cycloid as the tire rolls. The tire rolls with a constant velocity $v=$  m/s.

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The position vector of the stone is,

\(\vec{r}(t)= R\left(\frac{vt}{R}-\sin(\frac{vt}{R})\right) \,\hat{x}+R\left(1-\cos(\frac{vt}{R})\right)\,\hat{y} \) [m].

What is the force on the stone at a time $t=$  seconds?

\( \vec{F}= \) \( \hat{x}+ \) \( \hat{y} \) [N].