FYKOS Year 30 Series 4 Problem 3 — bicone · FYKOS 30 #30.4.3

Physics · mechanics

Problem

Consider a wooden construction (shown in the picture) with its foundation in the shape of an isosceles triangle with a base of length

c=35\;\mathrm{cm}

. The height of the legs of this triangle increases towards the base with an angle

α=2°

with the flat ground. A bicone with opening angle

φ=40°

and height 2

h=40\;\mathrm{cm}

is placed in the vertex opposite the base, where the triangle has angle

β=70°

. When released, the bicone starts rolling „uphill“, that is in the direction of the increasing height of the legs. Explain why the bicone can roll uphill. Find the dependence of the position of the centre of mass on the distance covered by the bicone? What is the velocity of the bicone in the instant before it hits the base. How many turns will the bicone make before it hits the base? The bicone is initially placed horizontally on the construction in such a way that its centre of mass is exactly above the vertex opposite the base.

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