Banked Tracks (1 Viewer)

[replayee]

Argh is it when resolving forces. assuming everything standard

Vertically: NcosO = Fsin0 + mg or Ncos0 + Fsin0 = mg

Radially: Nsin0 + F cos0 = mv2/r or Nsin0 - Fcos0 = mv2/r

This one is Fitzpatrick This one is Arnold

Just a little confused thanx

 

[pLuvia]

It depends on which way you resolve the forces. As if the F was pointing towards the centre then it would be first one, if the F was pointing up the track then it would be the second one

 

[3li]

fk, i havent done banked tracks in ages
just to clarify, u take mv^2/r as a positive horizontal force towards the centre of motion right? so the net sum of the vectors pointed towards the centre = mv^2/r
i.e.

==> Nsin0 Fcos0 <== <== mv^2/r

wuld mv^2/r = Fcos0 - Nsin0

 

[replayee]

that doesnt help at all. lol

which one do i use if it doesnt specify??

 

[3li]

if it says vehicle travels at speed > design speed then for train the pressure is exerted on the outer rails on the outer wheels which gives friction F and so friction is travelling towards centre
for a bike it means the cyclist needs to lean further inward because track isnt steep enough so the friction is travelling towards centre

so in these cases u take Nsin0+Fcos0 = mv^2/r and Ncos0-Fsin0 = mg


if the vehicle travels at speed < design speed
i.e. train exerts pressure on inner wheel where friction is moving up the slope
or for a bike, the cyclist must lean outwards from normal to maintain its circular path so friction is travelling up the slope

so in these cases u take Nsin0-Fcos0 = mv^2/r and Ncos0 + Fsin0 = mg