QUESTION $3$ : RAIL TRACTION AND VEHICLE DYNAMICS

$3\mathrm{.}1$ A locomotive travel on a level track. It has a masis of $\backslash (60$ t $\backslash )$ and rolling resistance of $\backslash (85\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$t$\}\backslash ).$ The trucks attached to the locomotive have a mass of $430$ tand a rolling resistance of $\backslash (120\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$t$\}\backslash )$ the driving wheels support $\backslash (70\backslash \%\backslash )$ of the locomotive mass. The coefficient of friction betweein the wheels and rail is $0,26.$

Calculate:

$3\mathrm{.}1\mathrm{.}1$ The tractive resistance at a constant speed.

$3\mathrm{.}1\mathrm{.}2$ The drawbiar pull between the locomotive and trucks.

$3\mathrm{.}1\mathrm{.}3$ The acceleration force if the train begins to accelerate at $0,56$

$\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$

$3\mathrm{.}2$ A vehicle has a wheel base of $\backslash (2,9\backslash$mathrm$\{$~m$\}\backslash )$ and its centre of gravity is $700$ mm above road level. The centre of gravity is $\backslash (1,25\backslash$mathrm$\{$~m$\}\backslash )$ in front of the rear axle. The vehicle travels at a constant speed of $\backslash (90\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ on a level road and the coefficient of friction between the wheels and the road is $0,4.$ Neglect load transfer. Calculate the minimum distance in which the vehicle can be stopped when:

$3\mathrm{.}2\mathrm{.}1$ Only the front wheels brake.

$3\mathrm{.}2\mathrm{.}2$ Only the rear wheels brake.

$3\mathrm{.}2\mathrm{.}3$ Both front and rear wheels brake.

$3\mathrm{.}2\mathrm{.}4$ Find the ratio of $\backslash ($ N$\_\{$F$\}$: N$\_\{$R$\}\backslash )$ when all four wheels brake.

QUESTION $4$ : STATIC AND DYNAMIC BALANCIING

A rotating shaft carries four cisc $\backslash ($ A$,$ B$,$ C $\backslash )$ and $\backslash ($ D $\backslash )$ rigidly altached to it$.$ The mass centres are at $\backslash (100\backslash$mathrm$\{$~mm$\},200\backslash$mathrm$\{$~mm$\}\backslash )$ and $150$ mm respectively from the axis of rotation. The axial distance between the disc is $600$ mm $.$ If masses $\backslash ($ B$,$ C $\backslash )$ and $\backslash ($ D $\backslash )$ are $\backslash (10\backslash$mathrm$\{$~kg$\},5\backslash$mathrm$\{$~kg$\}\backslash )$ and $4$ kg respectively,

Take plane A as reference plane and all the distance to the right of A are regarded as positive.

calculate:

$[$a$]$ The minimum value of mass $\backslash ($ A $\backslash )$

$($b$)$ The relative angular positions of $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash )$ with respect to $\backslash ($ B $\backslash )$ taken in a Clockurre direction to eusure complete balance.