Banked Motion! (1 Viewer)

[HSCExamMarker]

When frictional force ranges from -uF to uF
Show a max speed v at which the particle can travel without slipping up the track.
v^2/Rg = tanx+u/1-utanx

This is a direct question from 1995 HSC
I hav answers..but it's not really clear to me..

Coz..i thought, to calculate the speed that does not affected by the tendency to slipping up or down, i simply discard F component and solve for v?

Another one..

A train is rounding a curve of radius 50m at 72km/h
(a) find the ratio of the horizontal thrust of the rails on the outer wheels to the
weight of the train

(b) At what angle should the track be inclined to the horizontal to eliminate this
thrust?

* How would u determine the signs of componenets? in both banked and conical problems..

 

[Trev]

72km/h = (72*1000)/60² = 20m/s.

Horizontal thrust : outer wheels is v²:rg = 20²:50*9.8 = 400:490 = 40:49.

Vertically: Ncosө-mg=F [but F=0 because there is no thrust] so Ncosө=mg(1)
Radially: Nsinө=mv²/r (2)
(2)/(1) gives tanө=v²/rg
ө=tan^-1(20²/50*9.8)
ө=39'14".

Hope that's right I suck at this stuff.

 

[redd]

* How would u determine the signs of componenets? in both banked and conical problems..

thats a good question not too sure myself, but from expereince conical is usually T+N for horizontal and t - n for vertical

dont know why, perhaps some1 more knowledgeable can shed some lite

 

[yrtherenonames]

If you draw thje forces diagram right, it's pretty clear that the horizontal motion is in the one direction, whilst the vertical is moving in oposite directions, hence +/-