FYKOS Year 35 Series 4 Problem 3 — pendular collisions · FYKOS 35 #35.4.3

Physics · mechanics

Problem

Two small marbles are attached to ends of strings of the same length (l=42.0 cml = 42.0\,\mathrm{cm}) and negligible mass. The other ends of both strings are attached to a single point. The marbles are of the same size, but they are made from the different materials. First one is made of steel (ρ1=7 840 kg⋅m−3\rho_1 = 7~840\,\mathrm{kg\cdot m^{-3}}) and second one is made of dural (ρ2=2 800 kg⋅m−3\rho_2 = 2~800\,\mathrm{kg\cdot m^{-3}}). Both marbles are initially at the angle 5∘5^\circ with respect to the equilibrium position, and after releasing them, they collide elastically. What is the maximum height the individual marbles reach after the collision? What is the result after the second collision?

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