Question

An object of mass m is released from rest at a height h above the surface of a table. The object slides along the inside of the loop-the-loop track consisting of a ramp and a circular loop of radius R shown in the figure. Assume that the track is frictionless.

The answer for this is 5/2*R

I'm searching for some other solutions..
maybe we could use this as an exchange thread..
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We release an oil drop of radius r in air. The density of the oil is 790 kg/m3. C1 and C2 for 1 atmosphere air at 20∘ C are 3.80 × 10−4 (kg/m)/sec and 0.71 kg/m3, respectively.

How small should the oil drop be so that the drag force is dominated by the linear term in the speed (in lectures we called this Regime I). In this regime, the terminal velocity is mg/C1r. [m is the mass of the drop].

r<<

Answer 1

found it by myself..

vterm << vcrit

m*g/(C1*r) << C1/(C2*r)

m=4/3*pi*r^2*d

d:density of oil

solve for r