FYKOS Year 28 Series 3 Problem 3 — we're going to bend · FYKOS 28 #28.3.3

Physics · mechanics

Problem

Trains, as it is commonly known, don't have a differential and so when they go through a turn the wheels must turn with the same angular velocity. Now assume that the wheels have a cylindrical shape. Thus when going through a turn one wheel has to go a longer path than the other. The axis will have torsion applied on it and in a certain moment the frictional force between the wheel and railway rail won't be large enough and one wheel will slip and the tension on the axis will fall to 0. Determine the distance the individual slippages between depending on the radius of

R_{z}

. The wheel has a raidus of

R

, the axis has a radius of osa

r

, the length of the axis is

L

, the elastic shear modulus of the axis is

G

(steel), wagon with

N

wheels has a mass of

M

and coefficient of static friction between wheels and rails

f

. Finally you can insert realistic values.

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