Question
You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘deathwell’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25m?

Answer

The motorcyclist does not drop down when he is at the uppermost point if centrifugal force on motorcyclist is greater or equal to the weight of motorcyclist. i.e. $\frac{\text{mv}^2}{\text{R}}\ge\text{mg}$ $\Rightarrow\text{v}\ge\sqrt{\text{rg}}$ The minimum speed of motorcyclist not to fall from uppermost point is given by, $\text{v}_\text{min}=\sqrt{\text{rg}}$ Here, given $\text{r}=25,$ $\text{g}=9.8\text{m/s}^2$ $\therefore\text{v}_\text{min}=\sqrt{25\times9.8}=15.7\text{m/s}$

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