When will the ball fly?

Classical Mechanics Level 2

A ball, modelled as a particle, sits on a smooth semicircle with a height \(h\) from the ground. There is a gravitational pull, \(g\), on the ball acting straight down. The ball slides down the side of the semicircle. The height at which the ball will slide of is \(k\). We have the relationship \[k=\frac{a}{b}h\] Where \(a\) and \(b\) are positive coprime integers. Find \(a+b\).

Details and Assumptions

  • Take \(g=9.8\ \mathrm{m}\ \mathrm{s}^{-2}\)

  • \(h\) is strictly less than the radius of the semicircle.


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