Helical descent

Classical Mechanics Level 2

A particle is exhibiting a circular orbit, of radius 4 m 4m around a (vertical) pole. If downward acceleration of gravity acts on it, and it is initially 10 m 10m above the ground, then what is the magnitude of its velocity, when it reaches the ground? If the answer in the form a a a\sqrt{a} , where a a is an integer, find the value of a a .

Take g = 10 m / s 2 g=10m/s^2 . Ignore air resistance. The particle orbits at constant velocity parallel to the x y xy plane. Angular velocity is 1 r a d / s 1 rad/s .


The answer is 6.

Charley Shi by Charley Shi , 19, New Zealand

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1 solution

Using energy conservation principle, we get 1 2 m v 2 = \dfrac{1}{2}mv^2= 1 2 m u 2 + m g h \dfrac{1}{2}mu^2+mgh where u = 4 , g = 10 , h = 10 u=4, g=10, h=10 . Therefore v = 6 √ 6 v=6√6

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