deriving the formula for velocity on a banked track (1 Viewer)

[neuvie]

where does the formula v=sqrt(gr tan theta) come from? i tried searching it up on google but it gives an explanation mentioning some laws we dont do, and when i asked my physics teacher i was told that its extremely unlikely or that we will pretty much never be asked to derive it, but i am just interested in knowing how it goes.

 

[wollongong warrior]

Equate forces parallel with the track
Equate forces perpendicular to the track
Ncos(theta) = ... -(1)
Nsin(theta) = ... -(2)
Divide (2) by (1)
Make v the subject

 

[Aeonium]

where does the formula v=sqrt(gr tan theta) come from? i tried searching it up on google but it gives an explanation mentioning some laws we dont do, and when i asked my physics teacher i was told that its extremely unlikely or that we will pretty much never be asked to derive it, but i am just interested in knowing how it goes.

you are meant to derive it before you use it though?

 

[neuvie]

you are meant to derive it before you use it though?

yeah we do learn to derive it i guess (i didnt pay much attention in class so here i am asking questions), then we typically just work it out in the derived form but then i often forget/dont understand how to derive it

 

[FudiddidoAdrian]

yeah we do learn to derive it i guess (i didnt pay much attention in class so here i am asking questions), then we typically just work it out in the derived form but then i often forget/dont understand how to derive it

where does the formula v=sqrt(gr tan theta) come from? i tried searching it up on google but it gives an explanation mentioning some laws we dont do, and when i asked my physics teacher i was told that its extremely unlikely or that we will pretty much never be asked to derive it, but i am just interested in knowing how it goes.

ok so you split the normal force which goes up against the objects mass and gravity.

using that photo you get

Nsintheta = mv^/r (Fc) centripetal force

Ncostheta = mg

then you rearrange Ncostheta = mg to get N= mg/costheta

sub N into First equation so it becomes mgtantheta (sin/cos) = mv^/r

then you solve for v and you should get the v=sqrt(grtantheta)

even tho i helped you derive it it is important for you to understand it step by step, you should watch someone like scienceready on yt as he goes over the hsc syllabus for phys, hope this helps!

 

[neuvie]

ok so you split the normal force which goes up against the objects mass and gravity.

using that photo you get

Nsintheta = mv^/r (Fc) centripetal force

Ncostheta = mg

then you rearrange Ncostheta = mg to get N= mg/costheta

sub N into First equation so it becomes mgtantheta (sin/cos) = mv^/r

then you solve for v and you should get the v=sqrt(grtantheta)

even tho i helped you derive it it is important for you to understand it step by step, you should watch someone like scienceready on yt as he goes over the hsc syllabus for phys, hope this helps!

thank you very much for your explanation! i had just watched the video about circular motion by scienceready today and now i noted it in my book, appreciate the replies everyone