Find the minimum height h that will allow a solid cylinder of mass m and radius rcyl to loop the loop of radius rloop. express h in terms of the radius rloop of the loop.

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Explanation:

We know that V= √gr-----------------------------------------------------------------------------------------------------------------------(**)

Energy at the top of the loop;

= 1/2×m×V^2 + mg(2r)-------------------------------------------------------------------(1).

Potential energy= mgh-------------------------------------------------------------------(2).

Equating equation (1) and equation (2), we have;

=> 1/2×m×V^2 + mg(2r)= mgh-------------------------------------------------------(3).

=> 1/2(gr)+g(2r) = gh------------------------------------------------------------------(4).

Also, mg =mV^2/R-r---------------------------------------------------------------------(5).

Therefore, h in terms of the radius rloop of the loop is;

h=5/2× r_loop.

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